On weak solutions of nonstationary boussinesq equations

Yoshiyuki Kagel

    Research output: Contribution to journalArticlepeer-review

    31 Citations (Scopus)

    Abstract

    We study weak solutions of the initial and boundary value problems of the Boussinesq equations which describe the natural convection in a viscous incompressible fluid. We construct a global weak solution for the initial velocity in L2 and the initial temperature in L1. We show that the temperature θ(x, t) of our weak solution is Hölder continuous in x for almost every t > 0. In general, it is not known whether weak solutions are unique or not. We show that weak solutions are unique if they are in some Lebesgue space. We show, moreover, that weak solutions are regular if they belong to the uniqueness class.

    Original languageEnglish
    Pages (from-to)587-611
    Number of pages25
    JournalDifferential and Integral Equations
    Volume6
    Issue number3
    Publication statusPublished - May 1993

    All Science Journal Classification (ASJC) codes

    • Analysis
    • Applied Mathematics

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