Strong solutions of the stochastic Navier-Stokes equations in $R^3$ Jong Kim 35Q3035R6060H15stochastic Navier-Stokes equationsstrong solutionsglobal solutions We establish the existence of local strong solutions to the stochastic Navier-Stokes equations in $\mathbb{R}^{3}$. When the noise is multiplicative and non-degenerate, we show the existence of global solutions in probability if the initial data are sufficiently small. Our results are extension of the well-known results for the deterministic Navier-Stokes equations in $\mathbb{R}^{3}$. Indiana University Mathematics Journal 2010 text pdf 10.1512/iumj.2010.59.3930 10.1512/iumj.2010.59.3930 en Indiana Univ. Math. J. 59 (2010) 1417 - 1450 state-of-the-art mathematics http://iumj.org/access/