Existence theory for the isentropic Euler equations
We establish an existence theorem for entropy solutions to the Euler equations modeling isentropic compressible fluids. We develop a new approach for constructing mathematical entropies for the Euler equations, which are singular near the vacuum. In particular, we identify the optimal assumption req...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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2003
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| _version_ | 1797067192231002112 |
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| author | Chen, G LeFloch, P |
| author_facet | Chen, G LeFloch, P |
| author_sort | Chen, G |
| collection | OXFORD |
| description | We establish an existence theorem for entropy solutions to the Euler equations modeling isentropic compressible fluids. We develop a new approach for constructing mathematical entropies for the Euler equations, which are singular near the vacuum. In particular, we identify the optimal assumption required on the singular behavior on the pressure law at the vacuum in order to validate the two-term asymptotic expansion of the entropy kernel we proposed earlier. For more general pressure laws, we introduce a new multiple-term expansion based on the Bessel functions with suitable exponents, and we also identify the optimal assumption needed to validate the multiple-term expansion and to establish the existence theory. Our results cover, as a special example, the density-pressure law p(ρ) = κ1 ργ1 + κ2 ργ2 where γ1, γ2 ∈ (1, 3) and κ1, κ2 > 0 are arbitrary constants. |
| first_indexed | 2024-03-06T21:52:50Z |
| format | Journal article |
| id | oxford-uuid:4be65332-d690-4d9b-8e25-f64deae98b1d |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T21:52:50Z |
| publishDate | 2003 |
| record_format | dspace |
| spelling | oxford-uuid:4be65332-d690-4d9b-8e25-f64deae98b1d2022-03-26T15:46:16ZExistence theory for the isentropic Euler equationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:4be65332-d690-4d9b-8e25-f64deae98b1dEnglishSymplectic Elements at Oxford2003Chen, GLeFloch, PWe establish an existence theorem for entropy solutions to the Euler equations modeling isentropic compressible fluids. We develop a new approach for constructing mathematical entropies for the Euler equations, which are singular near the vacuum. In particular, we identify the optimal assumption required on the singular behavior on the pressure law at the vacuum in order to validate the two-term asymptotic expansion of the entropy kernel we proposed earlier. For more general pressure laws, we introduce a new multiple-term expansion based on the Bessel functions with suitable exponents, and we also identify the optimal assumption needed to validate the multiple-term expansion and to establish the existence theory. Our results cover, as a special example, the density-pressure law p(ρ) = κ1 ργ1 + κ2 ργ2 where γ1, γ2 ∈ (1, 3) and κ1, κ2 > 0 are arbitrary constants. |
| spellingShingle | Chen, G LeFloch, P Existence theory for the isentropic Euler equations |
| title | Existence theory for the isentropic Euler equations |
| title_full | Existence theory for the isentropic Euler equations |
| title_fullStr | Existence theory for the isentropic Euler equations |
| title_full_unstemmed | Existence theory for the isentropic Euler equations |
| title_short | Existence theory for the isentropic Euler equations |
| title_sort | existence theory for the isentropic euler equations |
| work_keys_str_mv | AT cheng existencetheoryfortheisentropiceulerequations AT leflochp existencetheoryfortheisentropiceulerequations |