 0560 Vesselin Petkov
 Global Strichartz estimates for the wave equation with timedependent potentials
(431K, postscript)
Feb 9, 05

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. We obtain global Strichartz estimates for the solutions $u$ of the wave equation $(\partial_t^2  \Delta_x + V(t,x))u = F(t,x)$ for timeperiodic potentials $V(t,x)$ with compact support with respect to $x$. Our analysis is based on the analytic properties of the cutoff resolvent $R_{\chi}(z) = \chi (U(T)  zI)^{1} \psi_1,$ where $U(T) = U(T, 0)$ is the monodromy operator and $T > 0$ the period of $V(t,x).$ We show that if $R_{\chi}(z)$ has no poles $z \in \C,\: z \geq 1$, then for $n \geq 3$, odd, we have a exponential decal of local energy. For $n \geq 2$, even, we obtain also an uniform decay of local energy assuming that $R_{\chi}(z)$ has no poles $z \in \C,\: z \geq 1,$ and $R_{\chi}(z)$ remains bounded for $z$ in a small neighborhood of $0$.
 Files:
0560.src(
0560.keywords ,
stri17.ps )