Convergence Rate for Compressible Euler Equations with Damping and Vacuum

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.