The Lagrangian Averaged Navier-Stokes equation with rough data in Sobolev spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:403

Article

Pennington, Nathan

关键词: Navier-Stokes;    Lagrangian averaging;    Global existence;   

DOI  :  10.1016/j.jmaa.2013.02.003

来源: Elsevier

【 摘 要 】

The Lagrangian Averaged Navier-Stokes equation is a recently derived approximation to the Navier-Stokes equation. In this article we prove the existence of short time solutions to the incompressible, isotropic Lagrangian Averaged Navier-Stokes equation with low regularity initial data in Sobolev spaces W-s,W-p(R-n) for 1 < p < infinity. For L-2-based Sobolev spaces, we obtain global existence results. More specifically, we achieve local existence with initial data in the Sobolev space H-n/2p,H-p(R-n). For initial data in H-3/4,H-2(R-3), we obtain global existence, improving on previous global existence results, which required data in H-3,H-2(R-3). (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free