Strong pathwise solutions of the stochastic Navier-Stokes system

Abstract

We consider the stochastic Navier-Stokes equations forced by a multiplicative white noise on a bounded domain in space dimensions two and three. We establish the local existence and uniqueness of strong or pathwise solutions when the initial data takes values in H1. In the two-dimensional case, we show that these solutions exist for all time. The proof is based on finite-dimensional approximations, decomposition into high and low modes and pairwise comparison techniques.