Smoothing Properties and Scattering for the Magnetic Schrödinger and Klein–Gordon Equations in an Exterior Domain with Time-Dependent Perturbations

Abstract

This paper deals with the existence, smoothing properties and scattering of solutions to the magnetic Schrödinger and Klein–Gordon equations in an exterior domain with time-dependent small perturbations. Smoothing properties based on the resolvent estimates will reinforce the abstract scattering theory developed in \[8] (K. Mochizuki, in Proc. 6th ISAAC, World Scienti c Publishing, River Edge, NJ, 2009, 476–485), and our concrete problems are treated in this framework.