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

Article type: Research Article

Authors: Kian, Yavar

Affiliations: Université Bordeaux I, Institut de Mathématiques de Bordeaux, 351, Cours de la Libération, 33405 Talence, France. E-mail: Yavar.Kian@math.u-bordeaux1.fr

Abstract: We obtain global Strichartz estimates for the solution u of the wave equation ∂t2u−divx(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 zj∈C with |zj|≥1.

Keywords: time-dependent perturbation, non-trapping metric, Strichartz estimates

DOI: 10.3233/ASY-2010-0982

Journal: Asymptotic Analysis, vol. 68, no. 1-2, pp. 41-76, 2010