A computer-assisted proof on the stability of the Kolmogorov flows of incompressible viscous fluid

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:169

Article

Nagatou, K

关键词: numerical verification;    Kolmogorov flows;    stability;    infinite dimensional eigenvalue problems;   

DOI  :  10.1016/j.cam.2003.10.016

来源: Elsevier

【 摘 要 】

There exists a great number of references of bifurcations and stability for the Navier-Stokes equations. Only a few, however, provide a rigorous result which guarantees stability or instability. Our aim is to present a rigorous theorem which proves the stability of certain solutions arising in what is called the Kolmogorov problem. We accomplish this by the verified computation. The eigenvalue problem arising in the Kolmogorov problem is no, self-adjoint and, accordingly, it is quite difficult to treat theoretically. Our method is a numerical approach to deal with this difficulty and numerical examples are given as a demonstration. (C) 2003 Elsevier B.V. All rights reserved.

【 授权许可】

Free