A limit problem in natural convection

Yoshiyuki Kagei, Michael Růžička, Gudrun Thäter

研究成果: Contribution to journalArticle

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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.

元の言語英語
ページ(範囲)447-467
ページ数21
ジャーナルNonlinear Differential Equations and Applications
13
発行部数4
DOI
出版物ステータス出版済み - 12 1 2006

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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