# American Institute of Mathematical Sciences

December  2009, 25(4): 1333-1347. doi: 10.3934/dcds.2009.25.1333

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

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

Received  December 2008 Revised  May 2009 Published  September 2009

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.
Citation: Xiaojing Xu. Local existence and blow-up criterion of the 2-D compressible Boussinesq equations without dissipation terms. Discrete & Continuous Dynamical Systems - A, 2009, 25 (4) : 1333-1347. doi: 10.3934/dcds.2009.25.1333
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