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

TL;DR

This paper establishes the strong Feller property for the Markov semigroups of 2D and 3D Navier-Stokes equations driven by space-time white noise, ensuring well-posedness in certain function spaces.

Contribution

It applies Hairer's regularity structures to prove the strong Feller property for stochastic Navier-Stokes equations driven by space-time white noise.

Findings

Proves strong Feller property for 2D and 3D stochastic Navier-Stokes.

Ensures global well-posedness for 2D case starting from rough initial data.

Uses advanced regularity structures theory to analyze stochastic PDEs.

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 $\eta\in (-\frac{1}{2},0)$.