  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.
