On quasilinear Maxwell equations in two dimensions

Abstract

New sharp Strichartz estimates for the Maxwell system in two dimensions with rough permittivity and non-trivial charges are proved. We use the FBI transform to carry out the analysis in phase space. For this purpose, the Maxwell equations are conjugated to a system of half-wave equations with rough coefficients. For this system, Strichartz estimates are similarly derived as in previous work by Tataru on scalar wave equations with rough coefficients. We use the estimates to improve the local well-posedness theory for quasilinear Maxwell equations in two dimensions.

50 pages, accepted to Pure and Applied Analysis

References in corpus (1)

• Time-harmonic solutions for Maxwell's equations in anisotropic media and Bochner-Riesz estimates with negative index for non-elliptic surfaces

Cited by in corpus (3)

• Normal trace inequalities and decay of solutions to the nonlinear Maxwell system with absorbing boundary
• Dimensional Reduction in Quantum Optics
• Global Strichartz estimates for an inhomogeneous Maxwell system