Local energy decay and Strichartz estimates for the wave equat ion with time periodic perturbations

Vesselin Petkov (1)

1 IMB - Institut de Mathématiques de Bordeaux

We examine the memorphic continuaiton of the cut-off resolvent Rχ(z) = χ(U(T, 0) − z)−1χ, χ(x) ∈ C∞ 0 (Rn), where U(t, s) is the propagator related to the wave equation with non-trapping time-periodic perturbations (potential V (t, x) or a periodically moving obstacle) and T > 0 is the period. Assuming that Rχ(z) has no poles z with |z| ≥ 1, we establish a local energy decay and we obtain global Strichartz estimates. We discuss the case of trapping moving obstacles and we present some results and conjectures concerning the behavior of Rχ(z) for |z| > 1.

Domaines: Equations aux dérivées partielles [math.AP]

Vesselin Petkov. Local energy decay and Strichartz estimates for the wave equat ion with time periodic perturbations. Progress in Nonlinear Diff. Equations and their Applications, 2006, 69, pp.267-285. ⟨hal-00375031⟩