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

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

    All Science Journal Classification (ASJC) codes

    • Computational Mathematics
    • Applied Mathematics

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