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The nonlinear stability of the Maxwell-Born-Infeld System

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If you have a question about this talk, please contact Prof. Mihalis Dafermos.

The Maxwell-Born-Infeld (MBI) system is a nonlinear model of classical electromagnetism that was introduced in the 1930s. It is the unique model that is derivable from an action principle and that satisfies 5 physically compelling postulates. In this talk, I will use an electromagnetic gauge invariant framework to establish the existence of small-data global solutions to the MBI system on the Minkowski space background in 1 + 3 dimensions. The nonlinearities in the PDEs satisfy a version of the null condition, which means that they have special algebraic structure that precludes the presence of the “worst possible combinations” of terms. As a consequence, we are also able to show that the global solutions have exactly the same decay properties as solutions to the linear Maxwell-Maxwell system, which were derived by Demetrios Christodoulou and Sergiu Klainerman (1990). Our results complement the large-data blowup results for plane-symmetric MBI solutions, which were shown first by Yan Brenier (2002), and later by J. Speck (2008). As a byproduct of our analysis, we also show that the MBI system is hyperbolic in all field-strength regimes where the equations are well-defined.

This talk is part of the Partial Differential Equations seminar series.

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