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The incompleteness of the Born-Infeld model for non-linear multi-d Maxwell's equations
Author(s):
Wladimir
Neves;
Denis
Serre
Journal:
Quart. Appl. Math.
63
(2005),
343-367.
MSC (2000):
Primary 35Q60
Posted:
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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Additional Information:
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
PII:
S0033-569X-05-00964-6
Received by editor(s):
October 5, 2004
Posted:
April 19, 2005
Copyright of article:
Copyright
2005,
Brown University
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