Local energy decay and Strichartz estimates for the wave equation with time-periodic perturbations
نویسنده
چکیده
Abstract. We examine the memorphic continuaiton of the cut-off resolvent Rχ(z) = χ(U(T, 0)− z)χ, χ(x) ∈ C 0 (R), 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.
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