The nonlinear stability of the trivial solution to the Maxwell-Born-Infeld system

Jared Speck
2012 Journal of Mathematical Physics  
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 space background in 1 + 3 dimensions. Because the nonlinearities in the system satisfy a version of the null condition, we are also able to show that these solutions decay at exactly the same rates as solutions to the linear Maxwell-Maxwell system. In addition, we show that on any Lorentzian manifold, the MBI system is
more » ... hyperbolic in the interior of the field-strength regime in which its Lagrangian is real-valued.
doi:10.1063/1.4740047 fatcat:ptff6sdzmjdvdgcifzrowd2hjq