Abstract: I will review a number of recent results which jointly show that one-dimensional turbulence, described by the stochastic space-periodic Burgers equation with small positive viscosity, provides a surprisingly good model for Kolmogorov's K41 theory of turbulence and for some other relater results from the theory of hydrodynamical turbulence. This model also allows for a rigorous 1D interpretation of the Landau's objection to the universality of the K41 theory.
Bio: Sergei Kuksin is a Head Scientist at the Steklov Mathematical Institute, the Head of laboratory at the Mathematical Institute of the RUDN University and a senior researcher at Paris VII. His research deals with KAM theory in PDEs, PDEs involved with random perturbations, turbulence and statistical hydrodynamics, and elliptic PDEs for functions between compact manifolds.
In 1992 he was a plenary speaker at ECM in Paris. In 1998 he was an invited speaker at ICM in Berlin. He received the Lyapunov Prize from the Russian Academy of Sciences.
