Global Strichartz estimates for an inhomogeneous Maxwell system

TL;DR

This paper establishes global-in-time Strichartz estimates for the Maxwell system with divergence-free data under decay and non-trapping conditions, using resolvent estimates for the Helmholtz problem.

Contribution

It provides the first global Strichartz estimates for the inhomogeneous Maxwell system with specific decay and geometric conditions.

Findings

Proves global-in-time Strichartz estimates for Maxwell system

Uses resolvent estimates for Helmholtz problem

Requires decay and non-trapping assumptions

Abstract

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