  This paper concerns the Cauchy problem in R^d for the stochastic
Navier-Stokes equation \partial_tu=\Delta u-(u,\nabla)u-\nabla p+f(u)+
[(\sigma,\nabla)u-\nabla \tilde p+g(u)]\circ \dot W, u(0)=u_0,\qquad divu=0,
driven by white noise \dot 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.
