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Title: Local Energy Decay in Even Dimensions for the Wave Equation with a Time-Periodic Non-Trapping Metric and Applications to Strichartz Estimates
Authors: Kian, Yavar
Keywords: Time-Dependent Perturbation
Non-Trapping Metric
Local Energy Decay
Strichartz Estimates
Issue Date: 2010
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 35, No 4, (2010), 329p-370p
Abstract: We obtain local energy decay as well as global Strichartz estimates for the solutions u of the wave equation ∂t2 u-divx(a(t,x)∇xu) = 0, t ∈ R, x ∈ Rn, with time-periodic non-trapping metric a(t,x) equal to 1 outside a compact set with respect to x. We suppose that the cut-off resolvent Rχ(θ) = χ(U(T, 0)− e−iθ)−1χ, where U(T, 0) is the monodromy operator and T the period of a(t,x), admits an holomorphic continuation to {θ ∈ C : Im(θ) ≥ 0}, for n ≥ 3, odd, and to {θ ∈ C : Im(θ) ≥ 0, θ ≠ 2kπ − iμ, k ∈ Z, μ ≥ 0} for n ≥ 4, even, and for n ≥ 4 even Rχ(θ) is bounded in a neighborhood of θ = 0.
Description: 2000 Mathematics Subject Classification: 35B40, 35L15.
ISSN: 1310-6600
Appears in Collections:Volume 36, Number 4

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