Strichartz estimates for Maxwell equations in media: The partially anisotropic case

TL;DR

This paper establishes Strichartz estimates for Maxwell equations with rough, partially anisotropic media, leading to new well-posedness results for quasilinear Maxwell equations by combining phase space analysis and energy estimates.

Contribution

It introduces Strichartz estimates for Maxwell equations in media with less than three eigenvalues, advancing the understanding of solutions in partially anisotropic environments.

Findings

Proved Strichartz estimates for Maxwell equations with rough permittivities.

Demonstrated well-posedness results for quasilinear Maxwell equations.

Connected phase space analysis with energy estimates for new insights.

Abstract

We prove Strichartz estimates for solutions to Maxwell equations in three dimensions with rough permittivities, which have less than three different eigenvalues. To this end, Maxwell equations are conjugated to half-wave equations in phase space. We use the Strichartz estimates in a known combination with energy estimates to show the new well-posedness results for quasilinear Maxwell equations.