Dr. Mikhail Vishik

Biography

Mikhail Vishik received his Ph.D. from Moscow State University in 1980. He is a professor in the Department of Mathematics at the University of Texas at Austin and is also affiliated with the Oden Institute. His research interests encompass a wide range of areas within partial differential equations and fluid dynamics. Specifically, his work includes the uniqueness and existence theory for the Euler equations that govern ideal incompressible fluids, the development of functional spaces like wavelets, and the linear and nonlinear stability theory related to fluid motion. He also investigates the Navier-Stokes equations, particularly focusing on limits with vanishing viscosity, and non-selfadjoint spectral theory. His contributions to geometry, especially concerning SDiff and Arnold's theory, as well as his explorations into set-theoretic fluid dynamics, have been significant in his field. Additionally, he conducts research into asymptotic theory and quantum averages and is involved in the study of non-Archimedean analysis and p-adic L-functions.

Research Interests