The nonlinear stability of the trivial solution to the Maxwell-Born-Infeld system
In this article, we use an electromagnetic gauge-free framework to establish the existence of small-data global solutions to the Maxwell-Born-Infeld (MBI) system on the Minkowski spacetime background in 1+3 dimensions. Because the nonlinearities in the system have a special null structure, we are al...
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| Format: | Article |
| Language: | en_US |
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American Institute of Physics (AIP)
2013
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| Online Access: | http://hdl.handle.net/1721.1/80817 https://orcid.org/0000-0001-5020-3568 |
| _version_ | 1826200988560654336 |
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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 | In this article, we use an electromagnetic gauge-free framework to establish the existence of small-data global solutions to the Maxwell-Born-Infeld (MBI) system on the Minkowski spacetime background in 1+3 dimensions. Because the nonlinearities in the system have a special null structure, we are also able to show that these solutions decay at least as fast as solutions to the linear Maxwell-Maxwell system. In addition, we show that on any Lorentzian manifold, the MBI system is hyperbolic in the interior of the field-strength regime in which its Lagrangian is real-valued. |
| first_indexed | 2024-09-23T11:44:33Z |
| format | Article |
| id | mit-1721.1/80817 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:44:33Z |
| publishDate | 2013 |
| publisher | American Institute of Physics (AIP) |
| record_format | dspace |
| spelling | mit-1721.1/808172022-10-01T05:40:54Z The nonlinear stability of the trivial solution to the Maxwell-Born-Infeld system Speck, Jared R. Massachusetts Institute of Technology. Department of Mathematics Speck, Jared R. In this article, we use an electromagnetic gauge-free framework to establish the existence of small-data global solutions to the Maxwell-Born-Infeld (MBI) system on the Minkowski spacetime background in 1+3 dimensions. Because the nonlinearities in the system have a special null structure, we are also able to show that these solutions decay at least as fast as solutions to the linear Maxwell-Maxwell system. In addition, we show that on any Lorentzian manifold, the MBI system is hyperbolic in the interior of the field-strength regime in which its Lagrangian is real-valued. National Science Foundation (U.S.) (Grant DMS-0406951) National Science Foundation (U.S.) (Grant DMS-0807705) 2013-09-20T12:16:36Z 2013-09-20T12:16:36Z 2012-08 2011-07 Article http://purl.org/eprint/type/JournalArticle 00222488 http://hdl.handle.net/1721.1/80817 Speck, Jared. “The nonlinear stability of the trivial solution to the Maxwell-Born-Infeld system.” Journal of Mathematical Physics 53, no. 8 (2012): 083703. © 2012 American Institute of Physics https://orcid.org/0000-0001-5020-3568 en_US http://dx.doi.org/10.1063/1.4740047 Journal of Mathematical Physics Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Institute of Physics (AIP) MIT web domain |
| spellingShingle | Speck, Jared R. The nonlinear stability of the trivial solution to the Maxwell-Born-Infeld system |
| title | The nonlinear stability of the trivial solution to the Maxwell-Born-Infeld system |
| title_full | The nonlinear stability of the trivial solution to the Maxwell-Born-Infeld system |
| title_fullStr | The nonlinear stability of the trivial solution to the Maxwell-Born-Infeld system |
| title_full_unstemmed | The nonlinear stability of the trivial solution to the Maxwell-Born-Infeld system |
| title_short | The nonlinear stability of the trivial solution to the Maxwell-Born-Infeld system |
| title_sort | nonlinear stability of the trivial solution to the maxwell born infeld system |
| url | http://hdl.handle.net/1721.1/80817 https://orcid.org/0000-0001-5020-3568 |
| work_keys_str_mv | AT speckjaredr thenonlinearstabilityofthetrivialsolutiontothemaxwellborninfeldsystem AT speckjaredr nonlinearstabilityofthetrivialsolutiontothemaxwellborninfeldsystem |