Solution semiflow to the compressible Euler equations with damping. (English) Zbl 1473.35428
Summary: This paper is concerned with the 3D isentropic compressible Euler equations with damping in periodic domain. Inspired by the theory of Markov semigroups, we show the existence of solution semiflow which satisfies the standard semigroup property and minimizes the energy (maximizes the energy dissipation) among all dissipative solutions.
MSC:
| 35Q31 | Euler equations |
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
| 76N15 | Gas dynamics (general theory) |
| 76S05 | Flows in porous media; filtration; seepage |
| 76M60 | Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
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