Recollections of V. I. Yudovich 1. V. L. Berdichevsky

Transcription

1 Recollections of V. I. Yudovich 1 V. L. Berdichevsky It is profoundly sad that the time allocated in the first version of the Symposium program for the presentation of Victor Iosifovich Yudovich is used now for recollections of him. It is the honor for me to share some of my recollections. Nature is usually sparing of granting too many talents to one man, but sometimes something goes wrong (or right), and a man appears who, like V.I., is endowed with powerful, fast and inquisitive mind, healthy body, affability and selfless ego. V. I. could have been equally outstanding as a writer or an athlete or a physicist or a mathematician; he became the world s best expert in mathematical hydrodynamics. It seems that there was no subject in this area which he did not think of with the full capacity of his powerful mind. For any question in this area, he was able to give a state-of-the-art review with the valuable comments on what is doable and what is, most probably, wrong. In the 70 s, he seems to have been the only skeptic in the across-the-field euphoria on the potential brought by the notion of strange attractor in turbulence theory. Time proved him right. In contrast to most mathematicians, his intuition had considerable physical component and his arguments were often of purely physical nature. I do not know of anyone whose knowledge of fluid mechanics was deeper or broader. Each discussion with him was memorable and enlightening. A typical questionanswer session proceeded like this: You would ask a question. V. I. would reply Wait a minute, and go into deep thought. While thinking, he liked to walk around the room, smoking a cigarette or sipping coffee. In couple of minutes, he would say There are ten options and listed all of them and would continue The first nine are hardly probable. If you want, I ll explain to you why later. Now, we have 1 Talk at V. I. Yudovich Memorial Session, IUTAM Symposium on Hamiltonian dynamics, vortex structures and turbulence, Moscow, August 25-30,

2 to focus on this one. From the further discussion you recognize how deep was the analysis made during this couple minutes. There was a great deal of invisible work behind his erudition. Once, we discussed what makes a textbook a valuable one. We both admired with Bellman s Matrix Theory: By the way, V.I. noticed, I solved all the exercise problems in this book. You all know that a considerable portion of these problems are research problems, with references to the original papers. V. I. was an exceptional teacher. To give you a flavor of his lectures, I will cite one excerpt: The term pure imaginary number should be perceived as one word. One cannot say pure imaginary number is a number such that like one cannot say that St. Laurent s river is the river which. Pure imaginary number is not a number like St. Laurent s river is not a river, it is a sea bay. His lectures were full of such colorful comparisons and unexpected parallels. V.I. did not care for making his results widely known. Most of his recent publications are in absolutely unreachable sources, as he used to say, in the proceedings of the management of my home association. This was an unfortunate manifestation of one of the most attractive features of his personality which distinguished him from most players in the field: he loved science, not his role in science. I remember a lesson which I got in this regard. About twenty years ago, I found an exact relation between entropy and probability for finite-dimensional ergodic Hamiltonian systems. It was a generalization of Einstein s formula which turned out to be a limit relation for the systems with an infinite number of degrees of freedom. I valued Einstein s insights among the greatest ever made. Not surprisingly, I was proud. Telling V.I. about this result, I was probably puffing up my chest too evidently. V.I. immediately caught what was inappropriate and reacted in his usual ironic but benevolent manner: OK, OK, you just made it out (rasobralsja). This was quite precise description of what we all are doing: we make it out. Peter Lax, when he learned about V.I. s death, said: He was an original mathematician and a great man. I think original mathematician is an 2

3 underestimation, but the second statement is very much to the point: he was a great man, indeed. All those who knew V.I had this impression. His extraordinary personality has too many dimensions to be discussed in this brief talk, but the following episode seems telling a lot. When my daughter Jenia was about 20 years old, she asked me What is the meaning of life, if any? For a religious person the answer is given; for a nonreligious person, the answer needs to be found. I shared with her my view on the subject, but she was not satisfied. Then I began asking my friends the same question. Among others, I sent an with this question to V.I. (he has met Jenia). I collected quite an impressive herbarium of answers, all of which, however, can be split into just a few categories. The only answer which stood apart was given by V.I: It is meaningless to search for the meaning of life outside life. The meaning of life is in its every moment, in an incidental chat with a stranger, in a bad mood this morning, in a daughter s kiss, in a lucky thought solving a problem. And this is exactly how he lived, appreciating every moment of existence. And this is what attracted people to him. V.I. was quite sensitive to moral issues. One episode comes to mind in this regard. In 70 s or 80 s, a book on applied mathematics came out, which touched upon some subject matter of interest to V.I.. The book was not good, and V.I. wrote a negative review and was about to publish it. At this time, another negative review appeared, signed by a number of academicians with questionable moral reputation. V.I. decided not to publish his one; he said: I do not want to be in this company. If V.I. were in this room, I think he would find a way to stop my admiring talk. I remember how elegantly he did that during the banquet celebrating his 70 th birthday. Russian banquets differ from those in the West in that speeches, each followed by drinks, are the backbone of the entire event. There were many people, I guess over a hundred, and speeches followed one another almost without intermissions. Needless to say, all speeches were full of admiration and love for the hero of the day. V.I. found a very delicate way to play down the 3

4 solemn spirit of the event caused by these speeches: after each speaker had finished, he got up and tell a funny story about the speaker. I would like to continue in the spirit V.I. would certainly prefer and tell you three jokes: one he did not like, one he loved, and one which he authored. First, a joke which V.I. did not like. Several years ago, my former graduate students Alesha Fridlyand, Vladik Soutirine and I published a paper in Physical Review Letters. The last sentence of this paper was: The first two authors thank Chudo Sherry and Nakhal Blum for stimulating discussions. There is nothing special in this sentence for an English language reader. Chudo Sherry and Nakhal Blum sounds like first and last names of some persons. A reader who knows Russian immediately recognizes something unusual: the word Chudo in Russian means magnificent, magic, the word Nakhal means impudent, shameless. Behind this appreciation for stimulating discussions was the following. I had a dog, a girl by name Sherry, and Alesha had a dog, a boy by name Blum, and this is where Chudo Sherry and Nakhal Blum came from. V.I. did not like this joke. He said Well, this is just a one move joke. V.I. often used chess jargon; in particular, he used it to classify jokes. In chess, there are one move problems (to checkmate in one move), two move problems (to checkmate in two moves), etc Accordingly, he distinguished one move jokes, two move jokes, etc. It is easy to make a one move joke, much harder to make a two move joke, and three move jokes are exceptionally rare. By the way, it should be mentioned, that V.I. was an accomplished chess player. I think he played at the level of a chess Master. About two months prior to his death, I called him. It was Saturday night. He said proudly. I have just come back from the office. I had a visitor there, a chess Master. I won two games. Returning to the joke, I have a suspicion that V.I. did not like it not because it was a one-move joke, but because he was mentioned in the acknowledgements as well. One point supports such a suspicion: there were one move jokes which he liked. Here is an example. 4

5 When in 1999 it was announced that a small planet of our solar system was named after V.I. and got the name Yudovich, one of his pupils asked Is there a life on Yudovich? The author of this joke is Leonia Kurakin. Now a joke authored by V.I.. It was at a joint seminar of Mathematics Department and Department of Mechanical Engineering at the University where I work. V.I. was giving a talk. When the discussion turned to the non-existence of solutions of Navier-Stokes equations for infinite time, the terms like 2 L, W, etc. came up. I chaired the meeting and stopped V.I., reminding that half of the audience are engineers. OK, said V.I., How can one explain the non-existence of solutions of Navier-Stokes equations to engineers? It is easy. Imagine that you have a pail filled with water, and you describe the behavior of water by Navier- Stokes equations. But the pail has a hole. In a while, the water is gone and there is no solutions of Navier-Stokes equations after that. Is this a real mechanism for the loss of solvability? Perhaps, not. V.I. valued this joke because it was an improvisation. Russian poet Samuil Yakovlevich Marshak wrote in one of his verses: People write, and time erases. All these episodes of the past life will be gone with us. Is there anything that the time will not erase? We are not given the power to know. But I dare to make a guess: at least two things will remain - the notion of co-symmetry, and the indefinite existence of solutions of two-dimensional Euler s equations. And this is complemented by a life full of intellectual adventures, joie de vivre and heartfelt friendships. p p 5