Schrödinger-type Equation with the Data in Morrey Spaces

Abstract

In this paper we investigate the regularity properties of Schrödinger-type equations with the data in certain Morrey spaces. Under some assumptions, we obtain that if the data is not in certain Morrey space, then the solution is also not in certain Morrey spaces. Hence, if the data which acts on the system does not balance local regularity and global decay, then the solution does not either.