The limit Riemann solutions to nonisentropic Chaplygin Euler equations
We mainly consider the limit behaviors of the Riemann solutions to Chaplygin Euler equations for nonisentropic fluids. The formation of delta shock wave and the appearance of vacuum state are found as parameter ε\varepsilon tends to a certain value. Different from the isentropic fluids, the weight...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2020-12-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2020-0113 |
| _version_ | 1818716590119583744 |
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| author | Lin Maozhou Guo Lihui |
| author_facet | Lin Maozhou Guo Lihui |
| author_sort | Lin Maozhou |
| collection | DOAJ |
| description | We mainly consider the limit behaviors of the Riemann solutions to Chaplygin Euler equations for nonisentropic fluids. The formation of delta shock wave and the appearance of vacuum state are found as parameter ε\varepsilon tends to a certain value. Different from the isentropic fluids, the weight of delta shock wave is determined by variance density ρ\rho and internal energy H. Meanwhile, involving the entropy inequality, the uniqueness of delta shock wave is obtained. |
| first_indexed | 2024-12-17T19:21:40Z |
| format | Article |
| id | doaj.art-b02df038b68f4580a7ee4f0e531656e3 |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-17T19:21:40Z |
| publishDate | 2020-12-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-b02df038b68f4580a7ee4f0e531656e32022-12-21T21:35:29ZengDe GruyterOpen Mathematics2391-54552020-12-011811771178710.1515/math-2020-0113math-2020-0113The limit Riemann solutions to nonisentropic Chaplygin Euler equationsLin Maozhou0Guo Lihui1College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, P. R. ChinaCollege of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, P. R. ChinaWe mainly consider the limit behaviors of the Riemann solutions to Chaplygin Euler equations for nonisentropic fluids. The formation of delta shock wave and the appearance of vacuum state are found as parameter ε\varepsilon tends to a certain value. Different from the isentropic fluids, the weight of delta shock wave is determined by variance density ρ\rho and internal energy H. Meanwhile, involving the entropy inequality, the uniqueness of delta shock wave is obtained.https://doi.org/10.1515/math-2020-0113nonisentropic fluidsriemann solutionsdelta shockvacuum stateentropy inequality35l6535l6776n15 |
| spellingShingle | Lin Maozhou Guo Lihui The limit Riemann solutions to nonisentropic Chaplygin Euler equations Open Mathematics nonisentropic fluids riemann solutions delta shock vacuum state entropy inequality 35l65 35l67 76n15 |
| title | The limit Riemann solutions to nonisentropic Chaplygin Euler equations |
| title_full | The limit Riemann solutions to nonisentropic Chaplygin Euler equations |
| title_fullStr | The limit Riemann solutions to nonisentropic Chaplygin Euler equations |
| title_full_unstemmed | The limit Riemann solutions to nonisentropic Chaplygin Euler equations |
| title_short | The limit Riemann solutions to nonisentropic Chaplygin Euler equations |
| title_sort | limit riemann solutions to nonisentropic chaplygin euler equations |
| topic | nonisentropic fluids riemann solutions delta shock vacuum state entropy inequality 35l65 35l67 76n15 |
| url | https://doi.org/10.1515/math-2020-0113 |
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