Dispersive estimates for wave and Schrödinger equations with a potential in non-trapping exterior domains

2024/01/23 by Thomas Duyckaerts, Duyckaerts, Thomas, Jianwei Urban Yang +1
Engineering · Mathematics · #35B65 #35L05 #35P25 #35Q41 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2401.12608

openalex publication_date 2024/01/23 · openalex created_date 2024/01/25 · openalex updated_date 2026/07/28

Abstract

We prove resolvent estimates for a Schrödinger operator with a short-range potential outside an obstacle with Dirichlet boundary conditions. As a consequence, we deduce integrability of the local energy for the wave equation, and smoothing effect for the Schrödinger equation. Finally, for both equations, we prove that local Strichartz estimates for the free equation outside an obstacle imply global Strichartz estimates with a short-range potential outside the same obstacle. The estimates are all global in time, after projection on the continuous spectrum of the operator.

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