Two-dimensional Navier-Stokes equations driven by a space-time white noise (Q1865327)

The authors study the two-dimensional Navier-Stokes equations with periodic boundary condition 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. The authors first construct a stationary martingale solution. Moreover, the authors prove that, for almost every initial data with a measure supported by negative spaces, there exists a unique global solution in the strong probabilistic sense.