Stability of nontrivial solutions of the Navier-Stokes system on the three dimensional torus

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:172

Article

Mucha, PB

关键词: Navier Stokes equations;    Stokes system;    global solution;    large data;    stability;   

DOI  :  10.1006/jdeq.2000.3863

来源: Elsevier

【 摘 要 】

This paper examines the stability of nontrivial regular solutions to the Navier- Stokes equations on a three dimensional torus. It is shown that the W-r(2, 1)-norm of the perturbation can he controlled if its initial data are small enough in the L-2-norm. A key element of the proof is to apply the Marcinkiewicz theorem to obtain the estimate for the Stokes 54 system. In particular we prove the stability of unforced two dimensional flows. (C) 2001 Academic Press.

【 授权许可】

Free