Strong-Feller property for Navier-Stokes equations driven by space-time white noise

Abstract

In this paper we prove strong Feller property for the Markov semigroups associated to the two or three dimensional Navier-Stokes (N-S) equations driven by space-time white noise using the theory of regularity structures introduced by Martin Hairer in [Hai14]. This implies global well-posedness of 2D N-S equation driven by space-time white noise starting from every initial point in $C^\eta$ for $\eta\in (-\frac{1}{2},0)$.