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.