# Vsevolod Alekseevich Solonnikov

Professor Vsevolod Alekseevich Solonnikov, brilliant mathematician from St. Petersburg, Russia, was born in Leningrad in 1933. The scientific activity V.A. Solonnikov began in the late 1950s, when he graduated from the Leningrad University with honors degree. He defended his diploma thesis in 1957 under the supervision of Prof. O.A. Ladyzhenskaya, and, after that, was invited to join her research group at LOMI (Leningrad Branch of Steklov Mathematical Institute). Beginning with his first published paper, Vsevolod Alekseevich has obtained new interesting results in various fields of PDEs and function theory, many of which are now considered classical. In his PhD Thesis he studied boundary value problem for general elliptic systems as well as for stationary Stokes equations. Later in his Doctoral Thesis V.A. Solonnikov developed the theory of initial boundary value problems for general parabolic systems and also obtained the analogous results for the non-stationary Stokes system, which is not parabolic. At the same time, V.A. Solonnikov jointly with K.K. Golovkin obtained results of multipliers in Holder and Besov spaces, which enable them to prove extremely sharp estimates for solutions of many problems in mathematical physics. In 1970s, the main topics of scientific investigations of V.A. Solonnikov were in the field of mathematical fluid mechanics. His results about differential properties of solutions to stationary and non-stationary Navier-Stokes equation are well known to the international mathematical community. Later on, Professor V.A. Solonnikov, jointly with Prof. O.A. Ladyzhenskaya, obtained fundamental results concerning the solvability of Navier-Stokes equations in domains with non-compact boundaries. No less well-known are his results concerning free-boundary problems and results about Navier-Stokes equations in domains with singular boundaries, including the solution of the problem of a moving three-phase contact line for large capillary numbers. In 1980s and 1990^{sh} V.A. Solonnikov was studied the problem of the motion of a drop in its full generality, and investigated the stability of axially symmetric equilibrium figures of rotating fluids. Continuing to study the stability of equilibrium figures of rotating fluids, he built up the rigorous mathematical theory of stability of rotating incompressible fluids. His proof of the inverse Lagrange theorem for the problem of stability of equilibrium configurations of rotating capillary fluids may be regarded as the solution of a one-hundred-years old classical Liapunov’s problem.

Prof. V.A. Solonnikov has published more than 300 papers in the theory of PDEs and function theory. His results have substantially influenced generations of mathematicians. Scientists from many different countries openly acknowledge that they received a great impulse in their scientific activity after discussions and/or joint work with him. In this respect, it is also worth mentioning that, together with J. Heywood, K. Masuda and R. Rautmann he was co-organizer of a series of international conferences on the Navier-Stokes equations in Oberwolfach (Germany), which had a great influence on the development of the theory of mathematical hydrodynamics. In addition, he has won love and respect from his colleagues all over the world.

The scientific achievements of V.A. Solonnikov were highly appreciated by the international mathematical community: he became professor of Ferrara University (Italy), to celebrate his 70^{th}, 75^{th}, and 80^{th }jubilees international conferences were organized in Germany, Portugal, Italy, Poland and Russia. _{ }V.A. Solonnikov has also been visiting professor in many academic institutions, including University of Paderborn (Germany), University of Lisbon (Portugal), University of Zurich (Switzerland), Waseda University (Japan), University of Toulon (France) and many others. He was awarded the Humboldt prize (2003); the M.A. Lavrentjev prize of the Russian Academy of Sciences (2009), the L.B Chebyshev award of the government of St. Petersburg. He is (was) a member of the Editorial Board of several international scientific Journals, including SIAM Journal of Mathematical Analysis, Interfaces and free boundaries, Journal of Mathematical Fluid Mechanics, Annali dell’Universita di Ferrara, Advances in Mathematical Sciences and Applications, Differential Equations and others.

As of nowadays, Prof. V.A. Solonnikov is still scientifically very active and, as a broad-minded person, always ready to discuss and give his precious insights to most complicated and important mathematical problems.

The entire mathematical fluid mechanics community wishes Professor Solonnikov many more years of great contributions, as a natural continuation of his fundamental work over the past sixty-plus years!