Global Strichartz estimates for the wave equation with a time-periodic non-trapping metric

Abstract

We obtain global Strichartz estimates for the solution u of the wave equation ∂_t²u−div_x(a(t, x)∇_xu)=0 with time-periodic metric a(t, x) equal to 1 outside a compact set with respect to x. We assume a(t, x) is a non-trapping perturbation and, moreover, we suppose that there are no resonances z_j∈C with |z_j|≥1.