On the Regularity of the Semilinear Term on the Cauchy Problem for the Schrödinger Equation

Abstract

The regularity assumption on the semilinear term of the Schrödinger equation is considered in the class of Sobolev spaces. Based on the modification of the Strichartz estimate, the assumption is improved to the half value from below compared with the known result for the scaling critical semilinear term.