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Olga Alexandrovna Ladyzhenskaya (1922–2004) Susan Friedlander, Peter Lax, Cathleen Morawetz, Louis Nirenberg, Gregory Seregin, Nina Ural’Tseva, and Mark Vishik

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Olga Alexandrovna Ladyzhenskaya (1922–2004) Susan Friedlander, Peter Lax, Cathleen Morawetz, Louis Nirenberg, Gregory Seregin, Nina Ural’Tseva, and Mark Vishik Olga Alexandrovna Ladyzhenskaya (1922–2004) Susan Friedlander, Peter Lax, Cathleen Morawetz, Louis Nirenberg, Gregory Seregin, Nina Ural’tseva, and Mark Vishik Olga Alexandrovna La- from uniqueness of solutions of PDE to convergence dyzhenskaya died in her of Fourier series and finite difference approxima- sleep on January 12th, 2004, tion of solutions. She used functional analytic tech- in St. Petersburg, Russia, at niques to treat nonlinear problems using Leray- the age of eighty-one. She left Schauder degree theory and pioneered the theory a wonderful legacy for math- of attractors for dissipative equations. Develop- ematics in terms of her fun- ing ideas of De Giorgi and Nash, Ladyzhenskaya and damental results connected her coauthors gave the complete answer to Hilbert’s with partial differential equa- nineteenth problem concerning the dependence tions and her “school” of stu- of the regularity of the solution on the regularity dents, collaborators, and col- of the data for a large class of second-order ellip- leagues in Russia. In a life tic and parabolic PDE. She published more than 250 dedicated to mathematics articles and authored or coauthored seven mono- she overcame personal graphs and textbooks. Her very influential book The tragedy arising from the cat- Mathematical Theory of Viscous Incompressible aclysmic events of twentieth Flow, which was published in 1961, has become a century Russia to become one classic in the field. Her main mathematical “love” of that country’s leading was the PDE of fluid dynamics, particularly the mathematicians. Denied a Navier-Stokes equation. This equation has a long place as an undergraduate at and glorious history but remains extremely chal- university, she was an exceptionally gifted young lenging: for example, the issue of existence of phys- girl, but one whose father disappeared in Stalin’s gulag. She eventually became a leading member of ically reasonable solutions to the Navier-Stokes the Steklov Institute (POMI) and was elected to the equations in three dimensions was chosen as one Russian Academy of Science. Her mathematical of the seven millenium “million dollar” prize prob- achievements were honored in many countries. lems of the Clay Mathematical Institute. (The CMI She was a foreign member of numerous acade- website gives a description by Fefferman of the mies, including the Leopoldina, the oldest German prize problem.) The three-dimensional problem academy. Among other offices, she was president remains open to this day, although it was in the of the Mathematical Society of St. Petersburg and, 1950s that Ladyzhenskaya obtained the key result as such, a successor of Euler. of global unique solvability of the initial boundary problem for the two-dimensional Navier-Stokes Ladyzhenskaya made deep and important con- equation. She continued to obtain influential results tributions to the whole spectrum of partial differ- and to raise stimulating issues in fluid dynamics, ential equations and worked on topics that ranged even up to the days before her death. 1320 NOTICES OF THE AMS VOLUME 51, NUMBER 11 Selected Honors of Olga Ladyzhenskaya This memorial article contains brief surveys of 1969 The State Prize of the USSR some of Ladyzhenskaya’s significant mathematical 1985 Elected a foreign member of the Deutsche Akademie achievements by two of her collaborators in St. Pe- Leopoldina tersburg, Gregory Seregin and Nina Ural’tseva. 1989 Elected a member of the Accademia Nazionale dei Lincei These are followed by “memories” of Olga Alexan- 1990 Elected a full member of the Russian Academy of Science drovna by other distinguished mathematicians who 2002 Awarded the Great Gold Lomonosov Medal of the Russian have known her and her work for many years, Academy namely Peter Lax, Cathleen Morawetz, Louis Niren- 2002 Doctoris Honoris Causa, University of Bonn berg, and Mark Vishik. Olga Alexandrovna was a woman of great charm and beauty. We are very grateful to Tamara Rozhkovskaya for presenting some of the lovely photographs of Olga that appear in the two volumes in honor of the eightieth birthday of Ladyzhenskaya edited by Rozhkovskaya, who is a “mathematical grandchild” of Olga and editor and publisher of the International Mathematical Series in which these volumes appear. At the conclusion of her appreci- ation article in the second of these two volumes, Nina Ural’tseva ( a “mathematical child” and close friend and collaborator of Olga ) writes “In the Sci- ence Museum in Boston there is an exhibition de- voted to mathematics. The names of the most in- fluential mathematicians of the 20th century are carved on a large marble desk…and Olga La- dyzhenskaya is among them”. —Susan Friedlander Left to right, Nina Ural’tseva, Olga Ladyzhenskaya, V. Smirnov. for them. The eminent mathematician V. Smirnov; the great pianist and professor of the Academy of Gregory Seregin and Nina Ural’tseva Music, N. Golubovskaja; the distinguished world- Olga Alexandrovna Ladyzhenskaya passed away famous poets A. Akhmatova and J. Brodsky; and quite unexpectedly on January 12 this year. She was the famous writer A. Solzhenitsyn are found among in good spirits two days before that. She had just them. sketched a paper on some computational aspects Her influence on twentieth century mathemat- in hydrodynamics and planned to finish it in ics is highly valued by the world scientific com- Florida. Olga was fond of sunlight; therefore, every munity. It was not only Olga’s scientific results, winter, the darkest period in our St. Petersburg, she though truly deep and fundamental, but also her longed for the South…. In her last years she had personal integrity and energy that played an es- serious problems with her eyes, and she suffered pecial role in her contribution to mathematics. enormously because of the winter darkness. She re- Olga’s focus in life was not limited to mathe- sisted such problems by all means, for example, matics and science. She was deeply interested in using special pencils when writing. She was to leave arts and intellectual life in general. She loved ani- for Florida on January 12. On the eve of January mals, was a passionate mushroom lover, and en- 11 she went to rest before her long trip and did not joyed flowers. She was an enthusiastic traveler and wake up. God gave her an easy death. had the wonderful skill of a storyteller when shar- Olga Ladyzhenskaya was a brilliant mathemati- ing her impressions with friends. cian and an outstanding person who was admired There were few things that did not touch her; by distinguished scientists, writers, artists, and she reacted keenly to any injustice, to the misfor- musicians, often becoming a source of inspiration tunes of others; and she helped lone and feeble peo- ple. She took this very personally. Susan Friedlander, is professor of mathematics at the Uni- versity of Illinois-Chicago. Her email address is She expressed openly her views on social mat- [email protected]. ters, even in the years of the totalitarian political Gregory Seregin is professor of mathematics at the St. Pe- regime, often neglecting her own safety. tersburg Department of the Steklov Institute. His email ad- Olga grew up during very hard times in Russia. dress is [email protected]. She was born on March 7, 1922, in the tiny town Nina Ural’tseva is professor of mathematics at St. Peters- of Kologriv in the north part of Russia. Her father, burg University, Russia. Her email address is uraltsev@ Alexander Ivanovich, taught mathematics in a high euclid.pdmi.ras.ru. school. Her mother, Anna Mikhailovna, kept house DECEMBER 2004 NOTICES OF THE AMS 1321 and looked after her husband fall of 1941 she worked as a teacher in the town and three daughters. Olga’s of Gorodets, and in the spring of 1942 she re- “grandfather”1, Gennady La- turned to Kologriv, where she took her father’s dyzhensky, was a famous position as a high school mathematics teacher. In painter. There were many October 1943 she finally became a student at books, including books on Moscow State University and graduated in 1947. history and fine arts, in their During these years, I. G. Petrovskii was her adviser. house. Books were almost the At that time she was strongly influenced by only source of cultural edu- Gelfand’s seminar. cation, because Kologriv was In 1947 Olga married A. A. Kiselev, a Leningrad too far from cultural centers. resident, so she moved there, with a recommen- The town was situated dation from Moscow State University to the grad- among wild forests, near the uate school of Leningrad State University (LGU). At picturesque river Unzha. All LGU S. L. Sobolev was appointed to be her scien- her life Olga carefully kept tific adviser. From the time she came to LGU, a very beautiful landscape paintings close friendship developed between Olga and V. I. Olga as a baby, with her father, by her grandfather, some of Smirnov and his family. In the fall of 1947 Smirnov, mother, and two sisters. them depicting fine views of at Ladyzhenskaya’s request, became head of a sem- the Unzha. inar on mathematical physics, which has been ac- It was in the summer of 1930 that Alexander tive ever since. The seminar brought together many Ivanovich decided to teach mathematics to his own mathematicians of the city working in the area of daughters. After he made partial differential equations and their applica- some explanation of the tions. Until her last days Ladyzhenskaya was one basic notions of geome- of the leading participants. try, he formulated a theo- rem and suggested that Finite-Difference Method and Hyperbolic his daughters prove it Equations themselves. It turned out Even the first results that Ladyzhenskaya obtained that the youngest one, in the late 1940s and in the early 1950s were a Olga, was the best of his breakthrough in the theory of PDEs.
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