Stability to the global large solutions of 3-D Navier-Stokes equations

In this paper, we consider the stability to the global large solutions of 3-D incompressible Navier-Stokes equations in the anisotropic Sobolev spaces. In particular, we proved that for any s(0) is an element of (1/2, 1), given a global large solution v is an element of C([0, infinity); H-0,H-s0(R-3) boolean AND L-3(R-3)) of (1.1) with del v is an element of L-loc(2)(R+, H-0,H-s0(R-3,)) and a divergence free vector w(0) = (w(0)(h), w(0)(3)) is an element of H-0,H-s0(R-3) satisfying parallel to w(0)(h)parallel to(H0,s) <= c(s,w03,v) for some sufficiently small constant depending on s is an element of (1/2, s(0)), v, and parallel to w(0)(3)parallel to(H0,s), (1.1) supplemented with initial data v(0) + w(0) has a unique global solution in u is an element of C([0, infinity); H-0,H-s0(R-3)) with del u is an element of L-2(R+, H-0,H-s0(R-3)). Furthermore, u(h) is close enough to v(h) in C([0, infinity); H-0,H-s (R-3)). (C) 2010 Elsevier Inc. All rights reserved.