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A limit problem in natural convection

  • Yoshiyuki Kagei
  • Michael Růžička
  • Gudrun Thäter
Article

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.

2000 Mathematics Subject Classification:

35K55 35Q35 76E19 76E20 80A1 

Keywords:

Natural convection dissipation Boussinesq limit 

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Copyright information

© Birkhäuser Verlag, Basel 2006

Authors and Affiliations

  • Yoshiyuki Kagei
    • 1
  • Michael Růžička
    • 2
  • Gudrun Thäter
    • 3
  1. 1.Faculty of MathematicsKyushu University 36FukuokaJapan
  2. 2.Applied Mathematics Inst.Freiburg UniversityFreiburgGermany
  3. 3.MathematicsDortmund UniversityDortmundGermany

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