Global-in-time Strichartz estimates for Schrodinger on scattering manifolds

Abstract

We study the global-in-time Strichartz estimates for the Schrödinger equation on a class of scattering manifolds $X^{\circ }$. Let ${\mathcal{L}}_V={\Delta }_g+V$ where ${\Delta }_g$ is the Beltrami-Laplace operator on the scattering manifold and $V$ is a real potential function on this setting. We first extend the global-in-time Strichartz estimate in Hassell-Zhang \cite{HZ} on the requirement of $V(z)=O(⟨z{⟩}^{-3})$ to $O(⟨z{⟩}^{-2})$ and secondly generalize the result to the scattering manifold with a mild trapped set as well as Bouclet-Mizutani\cite{BM} but with a potential. We also obtain a global-in-time local smoothing estimate on this geometry setting.

19 pages; Comments are welcome; Inhomogeneous Strichartz estimates are added

References in corpus (1)

• Semiclassical estimates in asymptotically Euclidean scattering