Remembering Professor Olga Alexandrovna Ladyzhenskaya Twenty Years On

It has been approximately twenty years since Professor Olga Alexandrovna Ladyzhenskaya passed away.

An eminent mathematician and member of several Academies of Science, passed away in January 2004. Her distinguished career was marked by significant contributions to partial differential equations, particularly the Navier–Stokes equations and nonlinear elliptic and parabolic equations.

Born in 1922 in Kologriv, Russia, Ladyzhenskaya’s passion for natural sciences was ignited by her father, a high school mathematics teacher. Tragically, he was executed by the NKVD in 1937, which led to Ladyzhenskaya being barred from Leningrad State University. Despite this, she persisted and graduated with honors from high school in 1939. She eventually studied at Pokrovskii Pedagogical Institute in Leningrad and later, at Moscow State University, graduating in 1947. That same year, she married A. A. Kiselev and joined Leningrad State University for graduate studies under the guidance of S. L. Sobolev.

Ladyzhenskaya’s academic journey continued as she became a postgraduate student under V. I. Smirnov and later led a seminar on mathematical physics and boundary-value problems. In 1953, she defended her habilitation dissertation at Moscow State University and in 1954, joined the Steklov Mathematical Institute in Leningrad. There, she collaborated with notable mathematicians and contributed significantly to the field of mathematical physics.

Her research focused primarily on two areas: the Navier–Stokes equations, and nonlinear elliptic and parabolic equations. In 1951, she proved a fundamental inequality for elliptic operators and explored the convergence of the Fourier method for hyperbolic equations. Her work in the late 1950s on the multiplicative inequality led to the proof of the existence of global unique solutions for two-dimensional Navier–Stokes systems. She also collaborated with A. A. Kisielev to demonstrate global existence in three-dimensional cases for small initial data and external forces. Ladyzhenskaya’s contributions extended to proving global existence of stationary and regular axially symmetric solutions to Navier–Stokes equations.

Her investigations into the regularity and uniqueness of weak Hopf solutions were groundbreaking. She showed that if a weak solution belongs to a specific function space, it is unique and regular. These achievements, along with her other work, were detailed in her monographs on Navier–Stokes equations and in collaboration with other mathematicians on nonlinear elliptic and parabolic equations.