Abstract
We consider the compressible Euler equations with damping. The singular behavior of the flow near vacuum and the large-time states are of particular interest. A class of solutions is constructed and shown to converge to the self-similar solutions of the porous media equation. The porous media equation is derived from the Euler equations through Darcy’s law. Thus we have justified Darcy’s law for the compressible flow time-asymptotically.
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Research supported in part by NSF and Army Basic Research Grants.
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Liu, TP. Compressible flow with damping and vacuum. Japan J. Indust. Appl. Math. 13, 25–32 (1996). https://doi.org/10.1007/BF03167296
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DOI: https://doi.org/10.1007/BF03167296