Compressible flow with damping and vacuum. (English) Zbl 0865.35107
The compressible Euler equations with damping and the singular behavior of the flow near the vacuum are discussed. The large-time behavior of solutions to the compressible Euler equations with damping and (related to it time asymptotically) to the so-called porous media equations is studied. A class of particular solutions for the compressible Euler equations which tend time-asymptotically to the Barenblatt solutions is constructed. The porous media equation is derived from the Euler equation through Darcy’s law.
Reviewer: O.Dementev (Chelyabinsk)
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
| 35B40 | Asymptotic behavior of solutions to PDEs |
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