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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.

MSC:
35Q35 PDEs in connection with fluid mechanics
76R10 Free convection
35B44 Blow-up in context of PDEs
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