Two-Dimensional Navier–Stokes Equations Driven by a Space–Time White Noise

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.