Global-in-time Strichartz estimates on non-trapping asymptotically conic manifolds

Abstract

We prove global-in-time Strichartz estimates without loss of derivatives for the solution of the Schroedinger equation on a class of non-trapping asymptotically conic manifolds. We obtain estimates for the full set of admissible indices, including the endpoint, in both the homogeneous and inhomogeneous cases. This result improves on the results in earlier papers of Hassell-Tao-Wunsch and Mizutani which were local in time.

40 pages, 2 figures. We have added some additional explanation concerning results used from earlier papers, particularly those related to the Legendre structure of the spectral measure

References in corpus (5)

• Strichartz estimates on Schwarzschild black hole backgrounds
• Strichartz estimates for the wave equation on manifolds with boundary
• Uniform Sobolev estimates for non-trapping metrics
• The fundamental solution and Strichartz estimates for the Schrödinger equation on flat euclidean cones
• Strichartz estimates for the Schrödinger equation on polygonal domains

Cited by in corpus (7)

• Strichartz estimates and wave equation in a conic singular space
• Uniform resolvent estimates for Schrödinger operator with an inverse-square potential
• Strichartz estimate and nonlinear Klein-Gordon on non-trapping scattering space
• Eigenvalue bounds for non-self-adjoint Schrödinger operators with non-trapping metrics
• Global in time Strichartz estimates for the fractional Schrödinger equations on asymptotically Euclidean manifolds
• The final state problem for the nonlinear Schrodinger equation in dimensions 1, 2 and 3
• Semiclassical limit of orthonormal Strichartz estimates on scattering manifolds