The global existence for the strong solution of the stochastic 3-D incompressible anisotropic Naiver-Stokes equations

Abstract

This paper considers the stochastic 3-D incompressible anisotropic Navier-Stokes equations. We establish the global existence of a strong solution in probability when either the horizontal component of the initial data and external force is sufficiently small or the horizontal viscosity coefficient is sufficiently large.