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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