Invariant measures for the stochastic Navier-Stokes Equations for compressible flows and the problem of turbulence

Speaker: Prof. Konstantina Trivisa，University of Maryland

Title: Invariant measures for the stochastic Navier-Stokes Equations for compressible flows and the problem of turbulence

Time & Venue: 2022.04.07 21:00-22:00 Zoom Meeting：924 888 5804  PW：AMSS2022

Abstract: In this talk I'll present results on the long-time behavior of solutions to a stochastically forced Navier-Stokes system, describing the motion of a compressible viscous fluid. In the one dimensional case, the existence of an invariant measure for the Markov process generated by strong solutions was established in collaboration with Michele Coti-Zelati and Nathan Glatt-Holtz. In that work, we overcome the difficulties of working with non-Feller Markov semigroups on non-complete metric spaces by generalizing the classical Krylov-Bogoliubov method, and by providing suitable polynomial and exponential moment bounds on the solution, together with pathwise estimates. The talk will conclude with a discussion on some recent developments on the multi-dimensional case for related models.