Abstract:
We use Gaussian measure on the N-dimensional space to define a stationary diffusion process on a  two-dimensional cone. This diffusion is the inviscid limit of the laws of the “enstrophy-energy” process for an N-dimensional Galerkin-Navier-Stokes type evolution with Brownian forcing and random stirring, this, regardless of the strength of the stirring. With the help of this two-dimensional diffusion process, we infer quantitative condensation bounds, which for suitable forcings show an attrition of all but the lowest modes in the inviscid limit. Based on joint work with Klaus Widmayer (U. Zurich).


Bio-Sketch：

Alain‑Sol Sznitman is French‑Swiss Professor Emeritus of Mathematics at ETH Zurich and 2023 elected member of the German National Academy of Sciences Leopoldina. His research lies in probability theory and mathematical physics, notably propagation of chaos, random media, random walks in random environments, and Random Interlacements. Before ETH Zurich, he worked at the Courant Institute (NYU) and CNRS (France). He has received major distinctions including the Rollo Davidson Prize (1991), the Line and Michel Loève International Prize in Probability (1999), and the Blaise Pascal Medal in Mathematics (2022). He has delivered plenary and invited addresses at major international congresses, and holds memberships in numerous academies and professional societies such as Academia Europaea, European Academy of Sciences and the American Mathematical Society (Fellow, inaugural class 2012).