Two-dimensional Navier-Stokes equations driven by a space-time white noise

Abstract

We study the two-dimensional Navier-Stokes equations with periodic boundary conditions perturbed by a space-time white noise. It is shown that, although the solution is not expected to be smooth, the nonlinear term can be defined without changing the equation. We first construct a stationary martingale solution. Then, we prove that, for almost every initial data with respect to a measure supported by negative spaces, there exists a unique global solution in the strong probabilistic sense. © 2002 Elsevier Science (USA).