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

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...

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Bibliographic Details
Published in:Communications in mathematical physics 2015-03, Vol.334 (3), p.1667-1679
Main Authors: Choi, Kyudong, Kiselev, Alexander, Yao, Yao
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Complex Systems
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
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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.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-014-2146-2