Blow-up criterion for the 2D Euler-Boussinesq system in terms of temperature

Date

2016-03-15

Authors

Qian, Chenyin

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Publisher

Texas State University, Department of Mathematics

Abstract

In this article, we study the blow-up solutions for the 2D Euler-Boussinesq equation. In particular, it is shown that if ∫T*0 sup r≥2 ∥Λ1-αθ(t)∥Lr/√r log r dt < ∞ or ∫T*0 ∥Λ1-αθ∥Ḃ0∞,∞ dt < ∞, then the local solution can be continued to the global one. This is an improvement of classical Lipschitz-type blow-up criterion (∥∇θ∥L1tL∞) in terms of the temperature θ.

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Keywords

2D Boussinesq equation, Blow-up criterion, Besov space, Transport equation

Citation

Qian, C. (2016). Blow-up criterion for the 2D Euler-Boussinesq system in terms of temperature. <i>Electronic Journal of Differential Equations, 2016</i>(73), pp. 1-11.

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Attribution 4.0 International

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