A limit problem in natural convection
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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 , 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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