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

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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.

Original languageEnglish
Pages (from-to)953-966
Number of pages14
JournalJournal of Computational and Applied Mathematics
Volume223
Issue number2
DOIs
Publication statusPublished - Jan 15 2009

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All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

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