Title: Invariant measures for the stochastic Navier-Stokes equations for compressible flows and the problem of Turbulence
Speaker: Prof. Konstantina Trivisa
University of Maryland Department of Mathematics and IPST
Abstract: Statistically stationary solutions to randomly forced systems have been of fundamental importance from both theoretical and practical points of view. From one hand the existence of invariant measures provides information on the long time dynamics of randomly forced systems and from the other, under certain ergodicity assumptions, it provides a link between experimental observations and theoretical predictions. In this talk I’ll present results on the long-time behavior of solutions to a stochastically forced one-dimensional Navier-Stokes system, describing the motion of a compressible viscous fluid. The existence of an invariant measure for the Markov process generated by strong solutions will be discussed.