Preprint 2003-028

Hydrodynamic structure of the augmented Born-Infeld equations

Yann Brenier

Abstract: The Born-Infeld system is a nonlinear version of Maxwell's equations. We first show that, by using the energy density and the Poynting vector as additional independent variables, the BI system can be augmented as a 1010 system of hyperbolic conservation laws. The resulting augmented system has some similarity with Magnetohydrodynamics (MHD) equations and enjoy remarkable properties (existence of a convex entropy, galilean invariance, full linear degeneracy). In addition, the propagation speeds and the characteristic fields can be computed in a very easy way, in contrast with the original BI equations. Then, we investigate several limit regimes of the augmented BI equations, by using a relative entropy method going back to Dafermos, and recover, the Maxwell equations for low fields, some pressureless MHD equations for high fields, and pressureless gas equations for very high fields.

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Yann Brenier, <>
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<> April 7 2003.

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