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| Entropies and Flux-Splittings for the Isentropic Euler Equations |
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Citation： |
CHEN Guiqiang,P. G. LEFLOCH.Entropies and Flux-Splittings for the Isentropic Euler Equations[J].Chinese Annals of Mathematics B,2001,22(2):145~158 |
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Net amount： 829 |
Authors： |
CHEN Guiqiang; P. G. LEFLOCH |
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| Abstract： |
The authors establish the existence of a large class of mathematical entropies (the so-called weak entropies) associated with the Euler equations for an isentropic, compressible fluid governed by a general pressure law. A mild assumption on the behavior of the pressure law near the vacuum is solely required. The analysis is based on an asymptotic expansion of the fundamental solution (called here the entropy kernel) of a highly singular Euler-Poisson-Darboux equation. The entropy kernel is only Holder continuous and its regularity is carefully investigated. Relying on a notion introduced earlier by the authors, it is also proved that, for the Euler equations,the set of entropy flux-splittings coincides with the set of entropies-entropy fluxes. These results imply the existence of a flux-splitting consistent with all of the entropy inequalities. |
Keywords： |
Compressible Euler equations, Real gas, Hyperbolic, Conservation law, Entropy, Euler-Poisson-Darboux equation |
Classification： |
35L65, 35L80, 76N10, 35L40, 65M12 |
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