Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



The incompleteness of the Born-Infeld model for non-linear multi-d Maxwell's equations

Authors: Wladimir Neves and Denis Serre
Journal: Quart. Appl. Math. 63 (2005), 343-367
MSC (2000): Primary 35Q60
DOI: https://doi.org/10.1090/S0033-569X-05-00964-6
Published electronically: April 19, 2005
MathSciNet review: 2150780
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Abstract: We study the Born-Infeld system of conservation laws, which is the most famous model for non-linear Maxwell's equations. This system is totally linear degenerated and there exists a conjecture, see Y. Brenier, Hydrodynamic structure of the augmented Born-Infeld equations, Arch. Rational Mech. Anal. 172 (2004), 65-91, that shocks are not allowed to form. In fact, we show that this conjecture is false and that the Born-Infeld model is not complete by itself. It means that a further theory is needed to complete the model.

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Wladimir Neves
Affiliation: Instituto de Matematica, Universidade Federal do Rio de Janeiro, C. Postal 68530, Rio de Janeiro, RJ 21945-970, Brazil
Email: wladimir@im.ufrj.br

Denis Serre
Affiliation: UMPA, Ecole Normale Superieure de Lyon, UMR 5669 CNRS, Lyon Cedex 07, France
Email: serre@umpa.ens-lyon.fr

DOI: https://doi.org/10.1090/S0033-569X-05-00964-6
Received by editor(s): October 5, 2004
Published electronically: April 19, 2005
Article copyright: © Copyright 2005 Brown University

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