ForeverMissed
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This memorial website was created in memory of our loved one, Charles Doering. We will remember him forever.
May 21, 2023
May 21, 2023
Charlie was a great scientist, a wonderful person, and had the ability to connect with others in very warm ways. Always kind and fun to be with. I wish I had spent more time together. We all miss you.
May 17, 2023
May 17, 2023
Yes, two years and the memories do not fade. Although our interests had diverged in recent years, much of the second half of my research career was bound up with Charlie. I learned more from him over the decades than from anyone else I can recall. I miss his good-natured interventions at meetings during which he had the gift of summarizing what needed to be said but with a kindness where no offence was taken. His name & work were mentioned continually at the encounters & meetings at the turbulence program at the Isaac Newton Institute last year (Jan-June 2022) in Cambridge.
May 15, 2023
May 15, 2023
Here in Portland, for the SIAM conference which for many years was held at Snowbird. Was chatting with Robert Krasny about mow much Charlie is missed. So far, this conference is rather dull. If Charlie were here, he would change that.
May 15, 2023
May 15, 2023
Linda, thank you for day's video - what a perfect Charlie tour of Ann Arbor! So much missed...
May 15, 2023
May 15, 2023
The chasm is at least partially filled by so many wonderful memories. 
May 15, 2023
May 15, 2023
Charlie, I want you to know we are doing well but we miss you every minute of the day and love you ten times.
September 28, 2021
September 28, 2021
Charlie had an extra dimension of communication and energy which often came out at gatherings with his friends. He was a Dead Head, so he could sing and play all the Grateful Dead songs. He was really quite good with the guitar and his voice was so friendly . . . listening to him play and sing made so many happy memories. Charlie and Paula came across the country to join Justine and my wedding ceremony in January 2004. A gathering of friends. Our wedding was on Saturday morning, and it snowed, so we had the whole day together with our friends. At the ceremony in Fuller Lodge, Charlie played and sang "Time in a bottle" and "Maybe I'm amazed". I'll never forget it. It was a peak moment for me. One more peak moment with Charlie to remember.
September 28, 2021
September 28, 2021
Saddened to learn of the passing of Charlie Doering. He had just joined the faculty at Michigan when I was a postdoc in the Mathematics department there. He showed much interest in my work, which was par for the course with him—always encouraging people at the beginning of their careers. I followed his research over the years after I left Michigan. His contributions were numerous and impactful. Beyond that, he was truly a good guy. It’s heartwarming to read these wonderful tributes.
September 10, 2021
September 10, 2021
I was so saddened and shocked to learn yesterday of Charlie's passing. He was my PhD advisor at Clarkson and was probably the most brilliant man I've ever had the privilege to know, be mentored by and work with during my graduate student career. His knowledge of Physics and Mathematics was phenomenal and he had a way of getting to the heart of any problem in an inspiring way. In addition to his very kind personality, he was very understanding and had a great sense of humor. My deepest sympathy to Paula and family.
June 18, 2021
June 18, 2021
Dear Family, Friends, and Colleagues of Charlie

Thanks to Darryl Holm for connecting me to this website. The tributes to Charlie are uplifting, and a reflection of the guy who always had a smile on his face and who loved life.....everything about life, and left no doubt about it. He was all in, and we were lucky to share whatever experiences we did with Charlie. The epitome of "one of a kind". He will be missed dearly, but more so he will be remembered dearly.  
June 13, 2021
June 13, 2021
Despite my overwhelming sadness in losing Charlie Doering, a lifelong friend from my days at Antioch College, who brought so much joy to so many; my grief has been ameliorated by the overwhelming appreciation voiced by so many of his students and associates in the University of Michigan community.

Charlie changed hearts and spirits through his with a rare combination of humor, generosity, keen intelligence, and an infinite enthusiasm for life. He is survived by his wonderful wife Paula, and their family, as well as a global community of admiring friends who will forever miss his warmth, energy, humor, honesty, and wit…
June 3, 2021
June 3, 2021
I first met Charlie in 1995 (Cambridge) and we have run into each other over and over since then. Such a pleasure to spend time with -- understatedly erudite and infectiously enthusiastic. I always looked forward to seeing him at Snowbird. Goodbye Charlie.
June 3, 2021
June 3, 2021
I don't remember when I first met Charlie, it feels like I've always known him. I've attended many of his lectures, at the same time inspiring and amusing, and I've chatted with him on math and world events; once he even gave me tips on how to handle traveling on (math) business with one of my kids. This was Charlie, someone you instantly felt at home with, an immediate friend. Amazingly upbeat.

I was happy to host him in Rio, he came for a workshop I organized, so much fun, and he gave a great talk -- "Wall to wall optimal transport". We chatted about the (soccer) World Cup, 2014, which was set to take place a month later in Brasil. He knew all about it!

Over the past year I had the privilege of working closely with Charlie -- we were both on the Organizing Committee for the new SIAM PDE webinar series. He was such a valuable member of this committee! He brought his own, rather original, point-of-view to the table and our work and the webinar was all the richer for it. Charlie was always immensely available, always happy to help, even when his health was failing him. During this past year, working with Charlie, I found out that I will miss him sorely.
June 2, 2021
June 2, 2021
It's been 44 years since I last saw Charlie. I had just looked him up on Fbook today, only to discover that I was too late. I never knew Charlie to be other than wide open to new thoughts and experiences, illuminatingly intelligent, transcendentally funny and always kind. We performed together in Modern Dance events. Love to all Charlie's loved ones. I'm sorry I missed him. 
May 30, 2021
May 30, 2021

We were very sad to hear about Charlie. I had met him about 20 years ago at a meeting in Santa Barbara. Since then, I had followed his work; and, over the last year, I had been interacting closely with him about the meeting at the Isaac Newton Institute.

Charlie inspired us and he will continue to do so.

My daughter, my wife, and I send our heartfelt condolences,



Rahul Pandit

May 29, 2021
May 29, 2021
Charlie was a much-needed source of wisdom and advice when I first came to Michigan as a new professor. He co-chaired the PhD theses of two of my students, and helped lead Kristin, a third student, through her candidacy exam four months ago. In my last email contact with Charlie, just one month ago, I updated him on the progress of one of the former students, now working as a postdoc elsewhere. Charlie was pleased to hear of Paige's progress, and said that he hoped to see me around the neighborhood. My house is one block over from the Doering household. Last September we sat together in his driveway and talked about the university response to COVID-19. Charlie was interested in everything. Another memory is seeing him early in the pandemic, while out on a walk. Charlie was on his famous bike, bringing carry-out from one of his favorite lunch places. He was always thinking of others, and we talked about helping businesses struggling from the pandemic. I will miss seeing him on my walks and I will miss his enthusiastic support in the workplace. Charlie was a great human being. 
May 27, 2021
May 27, 2021
Dr. Doering, Charlie, was a member of the dissertation committee of my student Linda Leckrone a couple of years ago. He was the most supportive committee member that we could have wished for. He cheered Linda, applauded her work, and supported her as she was also completing her master's in math. I will miss you; I send much love to all who are grieving his untimely death,
Vilma m.
May 27, 2021
May 27, 2021
It is special to read the tributes to Charlie, identifying the wide scope of his personal gifts: his humanity, his academic brilliance, and his teaching and leadership skill.  I saw all of these things in our limited interactions at UM over the years.  I valued our friendship and I always looked forward to seeing him. 
May 27, 2021
May 27, 2021
Charlie and I were contemporaries at the University of Texas. We were both young aspiring Ph.D. students. What I learned from Charlie then was the value of being kind and attentive to others. I am thankful we had the chance to reconnect before his passing and I was able to share what I will most remember about him. My condolences to Paula, his family, and the mathematical physics community that will surely miss him. 
May 26, 2021
May 26, 2021
Charlie was a great scholar and a warm and wonderful human being. Everything and everyone that came near him got some benefit from his passion for science and for life. Recently, and not knowing he was sick, I asked Charlie for some personal advice and, of course, he didn't just help me, he made my problem his own.
May 24, 2021
May 24, 2021
As a Ph.D. student, I read and learned from his textbook on Navier-Stokes equations. He was very nice to me on a few occasions I had the honor to meet him in person. He will be missed by many.
May 24, 2021
May 24, 2021
Charlie was, and still is, a major inspiration for me; not just in terms of mathematics, but it terms of a spirit of hope and optimism. Just being around him made you feel a sense of purpose, and that time was short and there was much to be done, and much to laugh about. 

A few months ago, he contacted me to tell me that Michigan was playing at Nebraska, and therefore we should plan to go. I knew about his health issues, and also the fall schedule was uncertain due to COVID, so I was slightly hesitant to plan. I believe he sensed this hesitation, and told me something I will never forget. He said, "Adam, the future is uncertain, but that is not going to stop me from planning for the best." 

A few years ago, when Nebraska played at Michigan, Charlie invited me out. Both he and Paula were amazingly gracious hosts, and we talked like like old friends even though I was only getting to know them. Before the game, Charlie took me on a bike tour in his Mr. Maize suit, meeting different groups of friends, and making many new friends on the way. Everyone lit up when they saw hi,. That was his effect on people, whether at a football game, a math conference, or just a casual conversation: his very presence reminded you of the lightness and joy within your own being.

Whenever life seems to have too much viscosity, I will remember Charlie, and the driving force of his unbreakable spirit.
May 24, 2021
May 24, 2021
Charlie enjoyed life and was passionate about science, music and practically everything he touched. He was very positive and always made everyone around him happy. He was a great family man and cared about people. May we all be comforted by the pleasant memories.
May 23, 2021
May 23, 2021
It is difficult to explain how important Charlie was for me…
Charlie was my Cicero, a model to imitate, my inspiration and motivation.
He is the one who made me understand that one can do both beautiful and useful research at the same time. The problems he has been proposing are hard, incredibly frustrating, but behind each (even partial) solution there is an important discovery. I remember when he was telling me “you might think it is numerology!” when trying to prove scaling laws.
I will never forget his enthusiasm for the mathematical proofs we were finding.
I will never forget his answers to the questions I was asking...those answers that do not make you feel bad. Actually, they really motivate you to find out more.
I will never forget the way he always tried to involve me in discussions and activities; with Charlie I always felt included, welcomed and that my efforts had some value in a way.
I will never forget his lectures and seminars. Although the topics he presented were always of great difficulty, one would never lose attention, because his talks where full of suspense, little jokes, some irony and those funny cartoons! A fantastic recipe and an incredible way to make an important message arrive.

Charlie, you have been so important for us younger researchers, and we will try our best to prove your conjectures and carry your messages.

Thank you Charlie!
May 23, 2021
May 23, 2021
Charlie was my postdoc advisor who welcomed me at UMich (’07-’08) and then took me to IMA in Minneapolis (’09-’11).  I consider those four years my happiest, most productive, and of course, the coldest, to date for which I am forever in his debt.  Besides the fact that my wife and I met in Ann Arbor and began seeing each other in Minneapolis when she got an internship there, I attribute a big part of my personal and academic growth to Charlie for he was a true scholar and above all, a tremendous human being. I don’t recall a single instance that he was not caring, inspiring, enthusiastic or optimistic, with probable exceptions when Michigan football lost to OSU (regularly) and when he broke his knees running from 1st to 2nd during our softball practice in Woods Hole. The family I met, Paula, Adrienne, Emily, Evan, Lil Vivi, the Cat, …, are just a wonderful gang and we shared interests on Korean food and tea beyond applied math.  

I really wish we’d talked more since I left the States.  Now there are several things I need to get on with to remember him by, first of which is to dig up the napkin he doodled math on several years back when we met for the last time for breakfast in Hong Kong.  I’m sure that everyone who has ever come to know him will be reminded of his charisma and accomplishments, in one way or another, for a very, very long time.
May 21, 2021
May 21, 2021
I knew Charlie when he was in his early 20s at Antioch College on the chorus tour where we sang Ockeghem in cathedrals all over Belgium, France and Italy. I was the shy one, he was the life of the party. I used to look at him and wonder.. how did he do that? He laughed and sang and danced and filled the room with laughter and love. Now that he's gone we get to do that for him. We can channel our innner Charlie. Let's fill the world with his gusto, joy and lust for life. He taught us how to do that!  You will be missed Charlie. The world is a better place for having had you here living life fully! Thank you.
May 21, 2021
May 21, 2021
I've enjoyed every single minute of his presentations.
He made many people happy. The world has lost a beautiful spirit.
Charlie is greatly missed.
May 20, 2021
May 20, 2021
John and I were remembering an evening at Clyde's with Charlie playing the guitar...such a good night. Saturdays will not be the same without him and his yellow suit.
Keeping you all in our hears and prayers
May 20, 2021
May 20, 2021
How wonderful to know Charlie. I met him in the mid 90s at one of his seminars. The topic was, you guessed it, upper bound theory, a subject close to my heart. Thereafter, Charlie enriched my life as a colleague and friend. I am grateful for his science, his joy and his kindness.
May 19, 2021
May 19, 2021
I remember Charlie as someone with unbounded energy. He just could not stay still. When we met, the first thing he would say was: "Let me show you something amazing". Then he would proceed with a short super-intense lecture on his current interest and its relation to other subjects. He was an applied mathematician of the highest caliber, attacking concrete problems with the full arsenal of pure mathematical methods, combined with physics and engineering intuition. His scientific horizon was vast, he saw connections to other subjects, he was inspired by real life problems. HIs optimism, both in scientific matters and in everyday life, was contagious. After a discussion with Charlie, I was always happy to go back to my problems that seemed hopeless before. I will miss his lectures, joint discussions, and friendship very much!
A M
May 19, 2021
May 19, 2021
When I think of Charlie, whom I have known for over 20 years, a famous Latin phrase from Virgil's Aeneid comes to my mind " sic itur ad astra", which loosely translates as " so one journeys to the stars", not only because Charlie loved convection and there is a lot of convection in stars, but more importantly because he reached the highest peaks with unwavering determination and contagious passion. He was a mentor and a friend and I will miss him so very much. Anna Mazzucato
May 19, 2021
May 19, 2021
I have so many memories of Charlie as a singular individual. He was so positive and inspiring. The enthusiasm he displayed in his talks was legendary: he gave carefully crafted, lively presentations that emphasized that he had a "showman" side, which I mean here as a huge compliment. His talks often had a thrilling mystery set up at the start, and an eventual punchline. Science and math would be better served if more people had his style and approachability. Luckily he has trained many young people to carry the torch.
May 18, 2021
May 18, 2021
I got to know Charlie & Paula through my husband Jean-Luc, for whom Charlie was a cherished mentor. They were such delightful, interesting, and fun company, and we had wonderful dinners in Woods Hole and Cambridge, UK. When I gave a talk on the furthest thing from fluid dynamics at Michigan (namely South Asian legal history), Charlie & Paula came! And when I was going through cancer treatment myself, they introduced me to the Zingerman's box. I am sorry that we are all taking turns, and that we have lost Charlie far too soon. I am so happy to have known him. Paula, you are in my thoughts.
May 18, 2021
May 18, 2021
Great scientist, excellent lecturer, extraordinary colleague. We will never forget you Charles.
May 18, 2021
May 18, 2021
Charlie was in Germany on a sabbatical when I was first getting to know the Doerings through Evan in 2005. I spent time with Paula and Emily and John and Adri and Tom and Sophie (no Vivi yet!), feeling very special to be in their fold at Woodlawn, before I ever met Charlie. I remember being worried before he returned to Ann Arbor - would my new boyfriend's dad be intimidating?? Ha! He was not. He was the warmest, most wonderful high school boyfriend's dad (a specific but important role!!) I ever could have known or spent time with. Charlie took Emily, John, Evan and I skiing in Colorado - brave man, him against 4 hormonal teens. I did not know how to ski and it is to his credit that I made it off the mountain - he was a kind and patient teacher (and most importantly, he bought me lessons...).
Paula and Charlie hosted me in Woods Hole several summers and some of my most beautiful memories of high school and growing up are from those visits.
When I left to go to college, I was heartbroken, to leave my family, Ann Arbor, my friends, Evan and his family. In my first week of school, desperately homesick, I checked my email and had a message from Charlie - a brief but loving "keep your chin up!" and a link to, what else, a Grateful Dead song. I wish I could remember what track it was. But it was exactly what I needed to get up and go to the caf.
He was so generous and one-of-a-kind and I will miss him so much.
Love to Paula, Evan, Emily, John, Arlo, Adri, Tom, Sophie, Vivi, and everyone else who will miss Charlie (so, everyone who ever met him).
Love,
Frannie
May 18, 2021
May 18, 2021
I feel so lucky to have gotten to know Charlie through his daughter, Emily. Charlie took me to my first UMich football game in September 2018 and I will forever cherish that memory. I know he was a genius of a thinker & teacher, but to me, he was always my friend's dad with the guitar and songs, amazing sense of humor, and jovial approach to life and learning. He loved his family so fiercely, and I loved seeing his love for his grandkids. Holding the whole Doering family in the Light and sending love and hugs as you celebrate a life so beautifully lived.
May 17, 2021
May 17, 2021
Charlie was an excellent scientist and a very nice person.
Each time we met, it was always a great pleasure to discuss with him.
We will miss him
May 17, 2021
May 17, 2021
Like all of us, I admired many of the important contributions of Charlie, who clearly was an exceptional member of our community. Sharing some memorable moments with him was a real privilege.

Charlie: you will not be forgotten -- we are already missing you...
May 17, 2021
May 17, 2021
We had lobster with Charlie and Paula years ago at Ashley's in Ann Arbor. Unforgettable fun. We are all way better off having known this funny, gentle, clever guy. Positive he's wearing that yellow suit in heaven now. Our love to all of his family and friends, there must be millions feeling the loss.
May 17, 2021
May 17, 2021
Whether gesturing with his telescopic pointer, posing for selfies with Michigan fans, or passing around a six-pack poolside on the roof at Snowbird, he was always Good Time Charlie. Simply a wonderful human being.
May 17, 2021
May 17, 2021
How did Charlie get into Applied Math? I had first met Darryl Holm in 1979 and visited LANL for 3 months in 1982 and each summer thereafter. In 1986 Darryl picked me up directly from the Ross Aviation flight at Los Alamos and said "Let's go into the CNLS because a new postdoc should be arriving this morning." There was Charlie, waiting patiently. I discovered he had come straight from Austin, having done a PhD with Cecile de Witt on stochastic QFT. That night he introduced me to Paula and Adrienne over dinner: "my girls", as he called them. I had been working in integrable systems for 15 yrs -- actually I was becoming bored -- so we apparently had little in common. Nevertheless, as we all know, Charlie has always had the knack of being able to draw people out, so the very first day we began to work on CGL. I'm sure I learned more from him than he did from me. Next summer (1987) we met Edriss Titi, Peter Constantin and Ciprian Foias at a meeting in Boulder and we realised the questions we had been asking about CGL were the big questions for Navier-Stokes. That was how Charlie "got into Applied Math", and fluid mechanics in particular. He continued to wear two hats, stat-physics and NSEs, for the rest of his career. 1986 was a long time ago and since that time we have been like brothers. I will miss him more than words can express.
May 17, 2021
May 17, 2021
In 1973 Charlie and I lived on the same hall in our first year at Antioch College. He was slender with long curly blond hair, wire rimmed glasses, trickster eyes and always smiling. I was thrilled to see that same smile in most of the pictures posted of him through the years. In retrospect what struck out to me was his enthusiasm for everything, any thing he was doing or we were going to do. He had the same enthusiasm for his lab project or going to a party or going out for donuts in the middle of the night.  It was always "oh this is going to be great, let's go, I can't wait, big fun." His joy was infectious, spread to everyone. We stayed friends through out college and I cannot recall a single instance where anyone was ever angry with Charlie. He got along with everyone. I do not remember him even getting upset with anyone. After school we lost touch, life gets in the way and we had no contact until I reached out to him when I heard he was sick. Had a few zoom calls in the last few months and he still had that same positive outlook. Our first zoom call he was literally in the hospital getting chemo treatments and he was still upbeat. I recall him smiling saying "look this is life, what are you gonna do. No you're not interrupting, thanks for the distraction, great to see you." Not an ounce of bitterness or resentment about what was happening to him, just sadness about not being around for his family. Wish there were more like him, more of us should model him. We miss you friend, thanks for the joy you gave us.
May 17, 2021
May 17, 2021
Charles was a great mathematician and physicist, and a very nice person. I will miss his "franc parler" and his honesty, along with his sharp mind, his clear and elegant demonstrations, publications and presentations.
May 17, 2021
May 17, 2021
We were friends for 45 years. He was the best.  So many fun and zany times. From his hot pant shorts to his yellow suit.  Always there when you needed him. His brilliance didn’t prevent him from connecting to people without judgement. He was a remarkable human being and I will miss him terribly.  My heart breaks for his family. He loved them so and he was lucky to have been loved by so many. 
May 17, 2021
May 17, 2021
Charlie was a wonderful and inspiring person. He gave a seminar in mechanical engineering a few years ago at Imperial College London and I noticed that the entire audience was smiling. Those smiles were the result of Charlie's enthousiasm, humor and mastery of his topic. We will miss you dearly.
May 17, 2021
May 17, 2021
To me, Charlie represented scientific courage and believe in own strength. As an example, he kept mathematical honesty connected to an applied field as fluid mechanics. His presentations were very inspiring and had an unforgettable lightness and fun about them. On a personal level, he could connect immediately and show he really cared, adding optimism and expertise. He could connect people, at the very least with his joy of music. I will be happy to keep his memory alive.
May 17, 2021
May 17, 2021
Charlie brought me to Los Alamos (CNLS). He left for Univ. of Michigan soon after but we remained good friends over many years. What a fun person to be around! This is a shock to me. I was not aware of his illness. You will be missed Charlie! - Sandip
May 16, 2021
May 16, 2021
Charlie was so fun! He was great company!
And isn't that the purpose of being human?
May 16, 2021
May 16, 2021
I am deeply saddened to hear about the passing of Professor Charlie Doering, a great scientist, mathematician and an amazing human being. It was a privilege to know Charlie and be considered a friend. He carried a warm halo of friendship and inner glow around him. His passion for life (family, mathematics, football; or is it family, football, mathematics?) has rendered him bigger than it. He is now forever one with the infinite. Rest in peace Charlie. We will miss you dearly.
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Recent Tributes
May 21, 2023
May 21, 2023
Charlie was a great scientist, a wonderful person, and had the ability to connect with others in very warm ways. Always kind and fun to be with. I wish I had spent more time together. We all miss you.
May 17, 2023
May 17, 2023
Yes, two years and the memories do not fade. Although our interests had diverged in recent years, much of the second half of my research career was bound up with Charlie. I learned more from him over the decades than from anyone else I can recall. I miss his good-natured interventions at meetings during which he had the gift of summarizing what needed to be said but with a kindness where no offence was taken. His name & work were mentioned continually at the encounters & meetings at the turbulence program at the Isaac Newton Institute last year (Jan-June 2022) in Cambridge.
May 15, 2023
May 15, 2023
Here in Portland, for the SIAM conference which for many years was held at Snowbird. Was chatting with Robert Krasny about mow much Charlie is missed. So far, this conference is rather dull. If Charlie were here, he would change that.
Recent stories

Simon & Garfunkel

May 18, 2021
Charlie had his guitar.
He played Simon and Garfunkel’s America. 
We visited his childhood home in upstate NY.
We laughed, drank and smoked.
He was my wingman and I his. 
Antioch was our playground.
He was 17
me 18.
We ruled.
May 18, 2021
Charlie’s Meyers-Briggs score was E S T J. This Meyers-Briggs category is called “the Entrepeneur”. Napoleon and Simon Bolivar were also E S T J's. It means that each time Charlie took on a physics or math question he would launch a proper campaign to get to know it,  get to know its relatives, other members of its family, listen to the question, get comfortable with it, ask it what it wanted, and eventually the question would tell him secrets that it hadn't ever told anyone else. 

For years at Los Alamos, in the CNLS we looked forward to our “August Summer Institute” working with Charlie, John Gibbon, Edriss Titi, Dave Levermore, Ciprian Foias and Peter Constantin. Our “Institute” would always rent a separate house for its August members, all living together. After a whole day interacting closely in mathematics discussions, in the late afternoon, Edriss would barbeque kebabs and Charlie would play the guitar, singing perhaps, sometimes going over to help Edriss supervise the kebabs, while we chatted on about today's possibilities, comfortable under the deep blue New Mexico sky during the best time of the day, when the shadows lengthen and one can see everything clearly. 

In about 1987, Charlie and I visited John Gibbon at Imperial College to continue our work on the CGL. Early each morning we took the 45-minute trip on the London Underground to South Kensington Station on the Piccadilly Line. Then we walked over to nearby Imperial College. Each evening, coming back late on the Underground we’d still be going over the day’s work, sitting together and doing what Charlie called “air board”, which meant writing formulas in the air together and commenting about the terms we were all writing in one of our familiar “air-equations”. Often, fellow passengers would stare at us, some perhaps thinking we were crazy and some perhaps wondering if our gestures were some kind of sign language, or perhaps even that our gestures were leaving something hanging in the air which only we could see.   

Remembering Charlie

May 16, 2021
As a young man, Charlie Doering’s life was focused on his work. Charlie was a consummate theorist, of great energy and ambition. His mind was churning with energy and ideas each morning when he awoke and it continued throughout the day.  

When Charlie was my postdoctoral colleague at Los Alamos during 1986-1988, his energy astounded me.  He was a dynamo. We once roomed together during a week-long trip. His constant flow of ideas and calculations that week literally wore me out.  Charlie matched his strength and energy against worthy and subtle problems. Charlie didn't attack problems.  Instead, he mounted campaigns against them with strategies and persistence worthy of Napoleon.  One of Charlie's great strengths and something that made him essentially unique was his facile combination of physical intuition and functional analysis.  

This unique combination inspired our work together when he was a postdoc at Los Alamos and we worked on the CGL (Complex Ginzburg Landau) equation. This nonlinear equation is ubiquitous and it has had a wide range of applications from fluids to nonlinear optics. So it was valuable to Charlie to know something about it. By this, I mean he had to know everything about it! 

One summer day in 1986, Charlie reported for his postdoctoral work at the Center for Nonlinear Studies at Los Alamos. On the morning of the day, John Gibbon and I had gotten some preliminary results about the CGL equation.  However, our results were quite incomplete. On that day, we just happened to leave my office as Charlie was walking down the hall to report for duty as a postdoc at the CNLS. John and I excitedly asked Charlie in the hallway whether he knew anything about CGL. Charlie answered, “Gentlemen, CGL is my life. I have just spent two years studying that equation.” 

Needless to say, after Charlie joined us, our CGL project had much more strength and focus.  Charlie would not let us stop until we got everything, including sharp optimal upper bounds on the Lyapunov dimension of the attractor, as well as optimal lower bounds on its dimension.  He kept pushing for improvement until he found a case in which these two bounds have the same power law and differed only by a constant shift. This was a dream result. However, Charlie kept raising the height of our goal higher and higher. Eventually, the bound on the Lyapunov dimension for CGL scaled with the number of NLS solitons that could fit into the domain. When we told that result to Ciprian Foias, Ciprian said, “Oh, congratulations!” That response from Ciprian would have been enough for me! However, Charlie immediately turned to taking the NLS limit and investigating its singularity formation in higher dimensions, or with higher nonlinearity. (By the way, NLS stands here for “nonlinear Schroedinger equation”, not “nonlinear studies”.)

Charlie’s campaign in the NLS project followed Leray's approach for singularity formation in the Navier-Stokes equations for fluid turbulance. Charlie was soon collaborating with the best analysts in the field, including Peter Constantin, Ciprian Foias, Dave Levermore, Edriss Titi, and others.  For example, Charlie and Peter Constantin spent five years on planar Couette flow and eventually obtained maxi-min results on the fractal dimension of its attractor for which the 1969 mini-max results of Howard et al. turned out to be an upper bound. Then Charlie continued his “obsession with convection” as he called it about the scaling laws for unstable Rayleigh-Besnard transport in a porous medium, which applies to the mechanism for carbon sequestration. Again, Charlie mounted a campaign and got to grips with this problem by using what he called, a “mother functional”. For more on this, see Charlie’s lecture video about it at https://www.youtube.com/watch?v=eDBHWU945Y8

Charlie, John, Peter, Dave, Edriss and I have followed each other and stayed in touch all through our careers, always trying to get together again like we did in the good old days of the “August Institute”. This was a meeting Charlie used to organise every year during August at Los Alamos. Eventually, an opportunity came for us to get him back to Los Alamos as the Deputy Director for the Center for Nonlinear Studies.  When Charlie returned to the CNLS, all of us felt the power increase immediately.  Charlie was very successful in attracting the best postdocs in his field from all over the world. Charlie also took over as Editor of the Nonlinear Science section of Physics Letters A.  As Editor of PLA, Charlie held the highest standards and brought great credit to that section of the journal which serves as part of his legacy.

Charlie's other great expertise, besides physics, fluid dynamics and functional analysis, was a particular branch of statistical physics that combines nonlinearity and stochastic processes. This burgeoning field of endeavor is often called ``nonequilibrium statistical mechanics.'' Charlie was a world leader in this field and he wrote some of its fundamental papers.  This work sustained Charlie's investigations into turbulence using stochastic analysis.  Charlie was well versed in this topic. In fact, one aspect of Charlie’s PhD thesis with Cecile De Witt at U Texas in Austin investigated the effects of adding noise to the Burgers equation. Charlie found that additive noise creates new solution behaviour for Burgers equation which was not present when either noise or nonlinearity were absent. This issue is still a hot topic in the theory of stochastic partial differential equations (SPDE). Charlie gave me SPDE lessons when he postdoc-ed with me. However, our CGL work with John absorbed all my attention at that time. Perhaps not surprisingly though, my own work now follows in his footsteps. 

Charlie's lecturing style was lucid and enthusiastic.  He sparked ideas as he spoke and often inspired his audience with his style of making new realizations while answering questions.  Often in answering a question Charlie finished by sketching out how this person's question led to an entire new research direction, for anyone who might care to pursue it. For example, Charlie lectured several times per  year for about five years during his work with Peter Constantin on the planar Couette problem.  Each time, Charlie laid out the program, told what had been known previously and then carried his audience to an appreciation of new, interesting, and substantial progress, finishing by revealing an exciting vista of the plethora of results which lay ahead. 

I am proud to have known Charlie Doering. If you want to know more, then just ask me next time you see me. I can tell you many stories about my personal experiences with the late, great Charlie Doering. Charlie was a great companion -- generous and fun. 

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