Global Strichartz estimates for an inhomogeneous Maxwell system

Abstract

We show a global in time Strichartz estimate for the isotropic Maxwell system with divergence free data. On the scalar permittivity and permeability we impose decay assumptions as $|x|\rightarrow\infty$ and a non-trapping condition. The proof is based on smoothing estmates in weighted $L^2$ spaces which follow from corresponding resolvent estimates for the underlying Helmholtz problem