Strichartz Estimates for Magnetic Schrödinger, Wave and Klein-Gordon Equations in Exterior Domain and Application to Scattering Theory

Abstract

Our purpose of this paper is to derive Strichartz estimates for solutions of magnetic Schrödinger, wave and Klein-Gordon equations in exterior to the star-shaped obstacle. For its proof we need the smoothing estimates for solutions of perturbed equations and the Strichartz estimates for solutions of free equations. Moreover as an application of them, we shall investigate the scattering theory for these equations with a power type nonlinearity in suitable space.