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

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Abstract

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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Authors and Affiliations

  1. Department of Mathematics, University of Wisconsin, Madison, WI, 53706, USA

    Kyudong Choi & Yao Yao

  2. Department of Mathematics, Rice University, Houston, TX, 77005, USA

    Alexander Kiselev

Authors
  1. Kyudong Choi
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  2. Alexander Kiselev
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  3. Yao Yao
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Correspondence to Kyudong Choi.

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Communicated by L. Caffarelli

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Choi, K., Kiselev, A. & Yao, Y. Finite Time Blow Up for a 1D Model of 2D Boussinesq System. Commun. Math. Phys. 334, 1667–1679 (2015). https://doi.org/10.1007/s00220-014-2146-2

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  • DOI: https://doi.org/10.1007/s00220-014-2146-2

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