On weak solutions of nonstationary boussinesq equations

Yoshiyuki Kagei

Research output: Contribution to journalArticle

28 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 - 1993

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Boussinesq Equations
Weak Solution
Global Weak Solutions
Lebesgue Space
Natural Convection
Viscous Fluid
Incompressible Fluid
Initial value problems
Initial Value Problem
Natural convection
Uniqueness
Boundary value problems
Boundary Value Problem
Temperature
Fluids

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

On weak solutions of nonstationary boussinesq equations. / Kagei, Yoshiyuki.

In: Differential and Integral Equations, Vol. 6, No. 3, 1993, p. 587-611.

Research output: Contribution to journalArticle

Kagei, Yoshiyuki. / On weak solutions of nonstationary boussinesq equations. In: Differential and Integral Equations. 1993 ; Vol. 6, No. 3. pp. 587-611.
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