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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:223

Article

Watanabe, Yoshitaka

关键词: Kolmogorov flows;    Computer-assisted proof;    Fixed-point theorem;   

DOI  :  10.1016/j.cam.2008.03.034

来源: Elsevier

【 摘 要 】

A computer-assisted proof of non-trivial steady-state solutions for the Kolmogorov flows is described. The method is based on the infinite-dimensional fixed-point theorem using Newton-like operator. This paper also proposes a numerical verification algorithm which generates automatically on a computer a set including the exact non-trivial solution with local uniqueness. All discussed numerical results take into account the effects of rounding errors in the floating point computations. (C) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

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