Local existence and blow-up criterion of the 2-D compressible  Boussinesq  equations without dissipation terms

Xiaojing Xu

doi:10.3934/dcds.2009.25.1333

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2009, Volume 25, Issue 4: 1333-1347. Doi: 10.3934/dcds.2009.25.1333

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Local existence and blow-up criterion of the 2-D compressible Boussinesq equations without dissipation terms

Xiaojing Xu^1,

1.
School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875

Received: November 30, 2008

Revised: April 30, 2009

Published: October 2009

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Abstract

In this paper, we consider the local existence and a blow-up criterion for smooth solutions to the 2-D isentropic compressible Boussinesq equations, and obtain some new commutator estimates. In particular, we show that the time integral of the spatial maximum of gradient of velocity controls the breakdown of smooth solutions.

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Mathematics Subject Classification: Primary: 35L60, 35Q35; Secondary: 76N10.

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Local existence and blow-up criterion of the 2-D compressible Boussinesq equations without dissipation terms

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