Entropies and flux-splittings for the isentropic Euler equations
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...
| 主要な著者: | , |
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| フォーマット: | Journal article |
| 言語: | English |
| 出版事項: |
2001
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| _version_ | 1826295444496449536 |
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| author | Chen, G LeFloch, P |
| author_facet | Chen, G LeFloch, P |
| author_sort | Chen, G |
| collection | OXFORD |
| description | 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 Hölder continuous and its regularity is carefully investigated. Relying on a notion introduced earlier by the authors, it is also proven 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. |
| first_indexed | 2024-03-07T04:01:08Z |
| format | Journal article |
| id | oxford-uuid:c49f19c6-e1f7-4e7b-954a-f6f36bc0f9e1 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T04:01:08Z |
| publishDate | 2001 |
| record_format | dspace |
| spelling | oxford-uuid:c49f19c6-e1f7-4e7b-954a-f6f36bc0f9e12022-03-27T06:24:47ZEntropies and flux-splittings for the isentropic Euler equationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:c49f19c6-e1f7-4e7b-954a-f6f36bc0f9e1EnglishSymplectic Elements at Oxford2001Chen, GLeFloch, PThe 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 Hölder continuous and its regularity is carefully investigated. Relying on a notion introduced earlier by the authors, it is also proven 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. |
| spellingShingle | Chen, G LeFloch, P Entropies and flux-splittings for the isentropic Euler equations |
| title | Entropies and flux-splittings for the isentropic Euler equations |
| title_full | Entropies and flux-splittings for the isentropic Euler equations |
| title_fullStr | Entropies and flux-splittings for the isentropic Euler equations |
| title_full_unstemmed | Entropies and flux-splittings for the isentropic Euler equations |
| title_short | Entropies and flux-splittings for the isentropic Euler equations |
| title_sort | entropies and flux splittings for the isentropic euler equations |
| work_keys_str_mv | AT cheng entropiesandfluxsplittingsfortheisentropiceulerequations AT leflochp entropiesandfluxsplittingsfortheisentropiceulerequations |