Abstract :
We obtain global Strichartz estimates for the solutions u of the wave equation (∂2
t − x + V (t, x))u =
F(t,x) for time-periodic potentials V (t,x) with compact support with respect to x. Our analysis is based
on the analytic properties of the cut-off resolvent Rχ (z) = χ(U(T ) − zI )−1ψ1, where U(T ) = U(T, 0)
is the monodromy operator and T >0 the period of V (t,x). We show that if Rχ (z) has no poles z ∈ C,
|z| 1, then for n 3, odd, we have a exponential decal of local energy. For n 2, even, we obtain also
an uniform decay of local energy assuming that Rχ (z) has no poles z ∈ C, |z| 1, and Rχ (z) remains
bounded for z in a small neighborhood of 0.
© 2005 Elsevier Inc. All rights reserved
