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

Yoshitaka Watanabe

doi:10.1016/j.cam.2008.03.034

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

Yoshitaka Watanabe

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	953-966
Number of pages	14
Journal	Journal of Computational and Applied Mathematics
Volume	223
Issue number	2
DOIs	https://doi.org/10.1016/j.cam.2008.03.034
Publication status	Published - Jan 15 2009

All Science Journal Classification (ASJC) codes

Computational Mathematics
Applied Mathematics

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10.1016/j.cam.2008.03.034

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abstract = "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.",

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