Emmy Noether Lectures

1994 Lecturer: Ol’ga Ladyzhenskaya

On Some Evolutionary Fully Nonlinear Equations of Geometrical Nature

O.A. Ladyzhenskayaas born on March 7, 1922 in Kologriv, a small town in Kostroma province. Her interest in mathematics developed under the influence of her father, Aleksandr Ivanovich Ladyzhenskii.
She graduated from the Moscow State University in 1947. The same year, due to family circumstances, Ladyzhenskaya moved to Leningrad. Since 1947 she has lived and worked in Leningrad, now St. Petersburg.
O.A. Ladyzhenskaya earned her PhD at the Leningrad State University in 1949, and her Doctor of Sciences degree at the Moscow State University in 1953. Since 1955 she has been Professor of Mathematics at the Physics Department of St. Petersburg University, and since 1961 the Head of the Laboratory of Mathematical Physics at the St. Petersburg Branch of the Steklov Mathematical Institute of the Academy of Sciences of Russia. In 1981 she was elected a corresponding member of the Academy of Sciences of Russia and in 1990 a full Member of the Academy. She is a member of the Deutsche Akademie der Naturforscher Leopoldina and of the Academia dei Lincei.
Ladyzhenskaya’s primary mathematical interests are in partial differential equations. She has made fundamental contributions to the theory of initial-boundary value problems for hyperbolic equations. Her results on the Navier-Stokes equations have become classical. Her monograph “The mathematical theory of viscous incompressible flow” is on the desk of every scholar working in theoretical hydrodynamics. Her paper “A dynamical system generated by the Navier-Stokes equations”, published in 1972, laid the foundations for the modern theory of attractors of dissipative systems. Since then, many people have contributed to the theory. However, the original approach developed by Ladyzhenskaya in the 1980s (see her recent book Attractors for semigroups and evolution equations, Cambridge University Press, 1991) is remarkably deep and powerful.
Yet another topic is among Ladyzhenskaya’s favorites: boundary value problems for quasilinear elliptic and parabolic equations. Since the mid-1950s, by herself and with her students, she has obtained a number of basic results in this field.
Her two books, one written with N.N. Ural’tseva, on elliptic equations, and another written jointly with Ural’tseva and V.A. Solonnikov, on parabolic equations, belong to the classics of literature on partial differential equations. In recent years, Ladyzhenskaya herself, and in collaboration with Ural’tseva, has obtained several new results for quasilinear and/or fully nonlinear elliptic and parabolic equations, giving detailed answers to some questions left unanswered in the above mentioned books.
Apart from mathematics, Ladyzhenskaya has broad interests in art, literature, and music. She is an enthusiastic nature-lover.
Ladyzhenskaya has a strong personality, in which charm matches an impressive intellectual power. A large circle of friends and associates in Russia know and rely on Ladyzhenskaya’s strength of conviction, her resilience, her warmth and generosity toward students and those in need of help.
Ladyzhenskaya gave a Special Noether Lecture at the JCM’94 meeting in Zurich on August 4, 1994.