Solution semiflow to the isentropic Euler system. (English) Zbl 1441.35164
The authors consider the compressible isentropic Euler equations in \(\mathbb R^N\) with periodic boundary conditions (so the domain is the flat torus) and focus on defining and establishing well-posedness of the system. Defining the semiflow concept as a mapping from the initial state to any state in a distributional sense, the authors prove it to possess the semigroup (Markovian) property. Such solution coincides with the strong solution if one exists and, also, maximizes energy dissipation.
Reviewer: Ilya A. Chernov (Petrozavodsk)
MSC:
| 35L65 | Hyperbolic conservation laws |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35D30 | Weak solutions to PDEs |
| 35Q31 | Euler equations |
Keywords:
multidimensional Euler equations; isentropic flow; well-posedness; solution semiflow; periodic boundary conditionsReferences:
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