Finite Time Blow Up for a 1D Model of 2D Boussinesq System

@article{Choi2015FiniteTB,
  title={Finite Time Blow Up for a 1D Model of 2D Boussinesq System},
  author={Kyudong Choi and A. Kiselev and Yao Yao},
  journal={Communications in Mathematical Physics},
  year={2015},
  volume={334},
  pages={1667-1679}
}
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. 

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