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Finite time blow up for a 1D model of 2D Boussinesq system. (English) Zbl 1309.35072
Summary: The 2D conservative Boussinesq system describes inviscid, incompressible, buoyant fluid flow in a gravity field. The possibility of finite time blow up for solutions of this system is a classical problem of mathematical hydrodynamics. We consider a 1D model of the 2D Boussinesq system motivated by a particular finite time blow up scenario. We prove that finite time blow up is possible for the solutions to the model system.

35Q35 PDEs in connection with fluid mechanics
76R10 Free convection
35B44 Blow-up in context of PDEs
Full Text: DOI arXiv
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