IUMJ

Title: Strong solutions of the stochastic Navier-Stokes equations in $R^3$

Authors: Jong Uhn Kim

Issue: Volume 59 (2010), Issue 4, 1417-1450

Abstract:

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 $\mathbb{R}^{3}$.