Open Access
2010 Initial Boundary Value Problem for Compressible Euler Equations with Relaxation
Qiangchang Ju, Yong Li, Ronghua Pan
Commun. Math. Anal. 8(3): 1-22 (2010).


In this paper, we study the global exisitence of $L^\infty$ weak entropy solution to the initial boundary value problem for compressible Euler equations with relaxtion and the large time asymptotic behavior of the solution. Motivated by the sub-characterisitic conditions, we proposed some structural conditions on the relaxation term comparing with the pressure function. These conditions are proved to be sufficient to construct the global $L^\infty$ entropy weak solution and to prove the equilibrium state is the global attactor of all physical weak solutions. Furthermore, the convergence rate is proved to be exponential in time. The proof is based on the entropy dissipation principle.


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Qiangchang Ju. Yong Li. Ronghua Pan. "Initial Boundary Value Problem for Compressible Euler Equations with Relaxation." Commun. Math. Anal. 8 (3) 1 - 22, 2010.


Published: 2010
First available in Project Euclid: 20 July 2010

zbMATH: 1194.35315
MathSciNet: MR2738331

Primary: 35L04 , 35Q35
Secondary: 35L65

Keywords: compensated compactness , compressible Euler equations , Entropy weak solutions , Large time behavior , relaxation

Rights: Copyright © 2010 Mathematical Research Publishers

Vol.8 • No. 3 • 2010
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