On quasilinear Maxwell equations in two dimensions

Abstract

New sharp Strichartz estimates for the Maxwell system in two dimensions with rough permittivity and nontrivial 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 proved using methods similar to those in previous works 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.