Special Session 158: From PDE control to the qualitative study of (random) dynamical systems

Level-3 large deviations for the white-forced 2D Navier--Stokes system in a bounded domain
Meng Zhao
CY Cergy Paris University
France
Co-Author(s):    
Abstract:
We study the large deviations principle (LDP) of Donsker-Varadhan type for the white-forced Navier-Stokes system in a bounded domain. Under the assumption that the noise is non-degenerate, we establish level-2 and level-3 LDPs with rate functions given by the Donsker-Varadhan formulas. The proof relies on an improved version of Kifer`s criterion, a lift argument, an improved abstract result on the large-time asymptotics of generalized Markov semigroups, and a delicate approximation scheme utilizing the resolvent operators of the Markov semigroup.