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 s0∈(1/2,1), given a global large solution v∈C([0,∞);H0,s0(R3)∩L3(R3)) of (1.1) with ∇v∈Lloc2(R+,H0,s0(R3)) and a divergence free vector w0=(w0h,w03)∈H0,s0(R3) satisfying ||w0h||H0,s ≥ cs.,w03, v for some sufficiently small constant depending on s ∈ (1/2,s0), v, and ||w03||H0, s, (1.1) supplemented with initial data v(0)+w0 has a unique global solution in u ∈ C ([0,∞);H0,s0(R3)) with ∇u ∈ L2(R+,H0,s0(R3)). Furthermore, uh is close enough to vh in C([0,∞);H0,s(R3)). © 2010 Elsevier Inc.
Gui, G., & Zhang, P. (2010). Stability to the global large solutions of 3-D Navier-Stokes equations. Advances in Mathematics, 225(3), 1248–1284. https://doi.org/10.1016/j.aim.2010.03.022