A priori estimates for solutions to the relativistic Euler equations with a moving vacuum boundary
We study the relativistic Euler equations on the Minkowski spacetime background. We make assumptions on the equation of state and the initial data that are relativistic analogs of the well-known physical vacuum boundary condition, which has played an important role in prior work on the non-relativis...
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group, LLC.
2020
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| Online Access: | https://hdl.handle.net/1721.1/126672 |
| _version_ | 1826189401199214592 |
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| author | Speck, Jared R. |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Speck, Jared R. |
| author_sort | Speck, Jared R. |
| collection | MIT |
| description | We study the relativistic Euler equations on the Minkowski spacetime background. We make assumptions on the equation of state and the initial data that are relativistic analogs of the well-known physical vacuum boundary condition, which has played an important role in prior work on the non-relativistic compressible Euler equations. Our main result is the derivation, relative to Lagrangian (also known as co-moving) coordinates, of local-in-time a priori estimates for the solution. The solution features a fluid-vacuum boundary, transported by the fluid four-velocity, along which the hyperbolicity of the equations degenerates. In this context, the relativistic Euler equations are equivalent to a degenerate quasilinear hyperbolic wave-map-like system that cannot be treated using standard energy methods. |
| first_indexed | 2024-09-23T08:14:28Z |
| format | Article |
| id | mit-1721.1/126672 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T08:14:28Z |
| publishDate | 2020 |
| publisher | Taylor & Francis Group, LLC. |
| record_format | dspace |
| spelling | mit-1721.1/1266722022-09-23T11:52:02Z A priori estimates for solutions to the relativistic Euler equations with a moving vacuum boundary Speck, Jared R. Massachusetts Institute of Technology. Department of Mathematics We study the relativistic Euler equations on the Minkowski spacetime background. We make assumptions on the equation of state and the initial data that are relativistic analogs of the well-known physical vacuum boundary condition, which has played an important role in prior work on the non-relativistic compressible Euler equations. Our main result is the derivation, relative to Lagrangian (also known as co-moving) coordinates, of local-in-time a priori estimates for the solution. The solution features a fluid-vacuum boundary, transported by the fluid four-velocity, along which the hyperbolicity of the equations degenerates. In this context, the relativistic Euler equations are equivalent to a degenerate quasilinear hyperbolic wave-map-like system that cannot be treated using standard energy methods. National Science Foundation (U.S.) (Grant DMS-1162211) National Science Foundation (U.S.) (Career Grant 454419) 2020-08-19T12:01:07Z 2020-08-19T12:01:07Z 2019-10 2019-11-20T19:25:11Z Article http://purl.org/eprint/type/JournalArticle 0360-5302 https://hdl.handle.net/1721.1/126672 Hadžić, Mahir, Steve Shkoller and Jarad Speck. “A priori estimates for solutions to the relativistic Euler equations with a moving vacuum boundary.” Communications in partial differential equations, vol. 44, no. 10, 2019, pp. 859-906 © 2019 The Author(s) en 10.1080/03605302.2019.1583250 Communications in partial differential equations Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Taylor & Francis Group, LLC. arXiv |
| spellingShingle | Speck, Jared R. A priori estimates for solutions to the relativistic Euler equations with a moving vacuum boundary |
| title | A priori estimates for solutions to the relativistic Euler equations with a moving vacuum boundary |
| title_full | A priori estimates for solutions to the relativistic Euler equations with a moving vacuum boundary |
| title_fullStr | A priori estimates for solutions to the relativistic Euler equations with a moving vacuum boundary |
| title_full_unstemmed | A priori estimates for solutions to the relativistic Euler equations with a moving vacuum boundary |
| title_short | A priori estimates for solutions to the relativistic Euler equations with a moving vacuum boundary |
| title_sort | priori estimates for solutions to the relativistic euler equations with a moving vacuum boundary |
| url | https://hdl.handle.net/1721.1/126672 |
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