Strichartz estimates for Maxwell equations on domains with perfectly conducting boundary conditions

Nicolas Burq; Robert Schippa

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arXiv · 2304.13368

Strichartz estimates for Maxwell equations on domains with perfectly conducting boundary conditions

Nicolas Burq·Robert Schippa

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Abstract

We consider Maxwell equations on a smooth domain with perfectly conducting boundary conditions in isotropic media in two and three dimensions. In the charge-free case we recover Strichartz estimates due to Blair--Smith--Sogge for wave equations on domains up to endpoints. For the proof we suitably extend Maxwell equations over the boundary, which introduces coefficients on the full space with codimension-$1$ Lipschitz singularity. This system can be diagonalized to half-wave equations amenable to the results of Blair--Smith--Sogge. In two dimensions, we improve the local well-posedness of the Maxwell system with Kerr nonlinearity via Strichartz estimates.

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Nicolas Burq, Robert Schippa. 2023-04-26. Strichartz estimates for Maxwell equations on domains with perfectly conducting boundary conditions. https://arxiv.org/abs/2304.13368

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