  We establish the existence and uniqueness of the maximal pathwise solution
for an abstract nonlinear stochastic evolutional equation, which takes the two
and three dimensional stochastic Navier-Stokes equations as a typical model,
forced by a multiplicative white noise, and show that the pathwise solution
exists globally in time in a positive probability when the initial data is
sufficiently small. Moreover, a global pathwise solution is obtained for the
stochastic Navier-Stokes equations defined on torus when the data is properly
regular and small.
