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

26Citations
Citations of this article
8Readers
Mendeley users who have this article in their library.

Abstract

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.

Cite

CITATION STYLE

APA

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

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free