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

Abstract

We study the global-in-time Strichartz estimates for the Schrödinger equation on a class of scattering manifolds X∘. Let where Δg 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 [23 Hassell, A., Zhang, J. (2016). Global-in-time Strichartz estimates on nontrapping asymptotically conic manifolds. Anal. PDE 9:151–192.[Crossref], [Web of Science ®] , [Google Scholar]] 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[4 Bouclet, J.M., Mizutani, H. Global in time Strichartz inequalities on asymptotically flat manifolds with temperate trapping, arXiv 1602.06287v1. [Google Scholar]] but with a potential. We also obtain a global-in-time local smoothing estimate on this geometry setting.

Locations

• Communications in Partial Differential Equations - View
• arXiv (Cornell University) - View - PDF