Global L2-solutions of stochastic Navier-Stokes equations

This paper concerns the Cauchy problem in R-d for the stochastic Navier-Stokes equation partial derivativetu = Deltau - (u, del)u - delp + f(u) + [(sigma, del)u - delp + g(u)] o W, u(0) = u(0), div u = 0, driven by white noise W. Under minimal assumptions on regularity of the coefficients and random forces, the existence of a global weak (martingale) solution of the stochastic Navier-Stokes equation is proved. In the two-dimensional case, the existence and pathwise uniqueness of a global strong solution is shown. A Wiener chaos-based criterion for the existence and uniqueness of a strong global solution of the Navier-Stokes equations is established.