Regularity properties of Schrodinger equations in vector-valued spaces and applications

Abstract

In this paper, regularity properties and Strichartz type estimates for solutions of the Cauchy problem for linear and nonlinear abstract Schrodinger equations in vector-valued function spaces are obtained. The equation includes a linear operator A defined in a Banach space E, in which by choosing E and A, we can obtain numerous classes of initial value problems for Schrodinger equations, which occur in a wide variety of physical systems.