Blow–up for nonlinear Maxwell equations

Piero d'Ancona (1) , Serge Nicaise (2) , Roland Schnaubelt

1 Sapienza University of Rome - Dipartimento di Matematica "Guido Castelnuovo" [Roma I]
2 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015

We construct classical solutions to the nonlinear Maxwell system with periodic boundary conditions which blow up in H(curl). A similar result is shown on the full space. Our construction is based on an analysis of a shock wave in one space dimension.

Mots clés: Quasilinear Maxwell system; blow-up; shock; Kerr model

Domaines: Mathématiques [math]

Piero d'Ancona, Serge Nicaise, Roland Schnaubelt. Blow–up for nonlinear Maxwell equations. Electronic Journal of Differential Equations, 2018, 2018 (73), pp.1-9. ⟨hal-03137619⟩