## Convergence rate for compressible Euler equations with damping and vacuum.(English)Zbl 1022.76042

Summary: We study the asymptotic behavior of $$L^\infty$$ weak-entropy solutions to compressible Euler equations with damping and vacuum. Previous works on this topic are mainly concerned with the case away from the vacuum and with small initial data. In the present paper, we prove that the entropy-weak solution strongly converges to the similarity solution of the porous medium equations in $$L^p(\mathbb{R})$$ ($$2\leq p<\infty$$) with estimated 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.

### MSC:

 76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics 35Q35 PDEs in connection with fluid mechanics 76S05 Flows in porous media; filtration; seepage
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