调和分析和偏微分方程研讨班：Strichartz estimates for wave equations with a potential in non-trapping exterior domains

中科院数学与系统科学研究院

数学研究所

调和分析及其应用研究中心

学术报告

调和分析和偏微分方程研讨班

报告人：杨建伟（北理工）

题  目：Strichartz estimates for wave equations with a potential in non-trapping exterior domains

时  间：2023.03.28（星期二）16:00-17:00

地  点：数学院南楼N913

摘  要：Consider the linear wave equations with a potential outside a compact set with a non-trapping boundary condition. Assuming that the potential satisfies an appropriate decreasing condition and that zero is not an eigenvlue or a resonance, we prove that the solution of the wave equation projected to the subspace associated to the continuous spectrum of the Schrödinger operator satisfies global Strichartz estimates. Our method is based on the local Strichartz estimate in exterior domains without potential, a result going back to Smith-Sogge, and the local energy decay which is obtained from a uniform resolvent estimate. This work is joint with Thomas Duyckaerts.