A limit problem in natural convection

Yoshiyuki Kagei, Michael Růžička, Gudrun Thäter

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We discuss a model limit problem which arises as a first step in the mathematical justification of our Boussinesq-type approximation [4], which takes into account dissipative heating in natural convection. We treat a simplified highly non linear system depending on a (perturbation) parameter ε. The main difficulty is that for ε ≠ 0 the velocity is not solenoidal. First we prove that our system has weak solutions for each fixed ε. Moreover, while the chosen perturbation parameter ε tends to zero we show, that we arrive at the usual incompressible case and the standard Boussinesq approximation.

Original languageEnglish
Pages (from-to)447-467
Number of pages21
JournalNonlinear Differential Equations and Applications
Volume13
Issue number4
DOIs
Publication statusPublished - Dec 1 2006

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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