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Archive for Rational Mechanics and Analysis

, Volume 166, Issue 4, pp 359–376 | Cite as

Convergence Rate for Compressible Euler Equations with Damping and Vacuum

  • Feimin Huang
  • Ronghua Pan

Abstract

 We study the asymptotic behavior of L weak-entropy solutions to the compressible Euler equations with damping and vacuum. Previous works on this topic are mainly concerned with the case away from the vacuum and small initial data. In the present paper, we prove that the entropy-weak solution strongly converges to the similarity solution of the porous media equations in L p (R) (2≤p<∞) with decay rates. The initial data can contain vacuum and can be arbitrary large. A new approach is introduced to control the singularity near vacuum for the desired estimates.

Keywords

Porous Medium Initial Data Asymptotic Behavior Decay Rate Convergence Rate 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Feimin Huang
    • 1
  • Ronghua Pan
    • 2
  1. 1.Institute of Applied Mathematics Academia Sinica Beijing, ChinaCN
  2. 2.Department of Mathematics University of Michigan Ann Arbor, MI 48109-1109 e-mail: panrh@umich.eduCN

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