Local and global strong solution to the stochastic 3-D incompressible anisotropic Navier-Stokes equations

Abstract

Considering the stochastic 3-D incompressible anisotropic Navier-Stokes equations, we prove the local existence of strong solution in H 2 (T 3 ). Moreover, we express the probabilistic estimate of the random time interval for the existence of a local solution in terms of expected values of the initial data and the random noise, and establish the global existence of strong solution in probability if the initial data and the random noise are sufficiently small.2010 Mathematics Subject Classification. Primary: 35Q35, 60H15; Secondary: 76B03.