Local well-posedness of the fractional inhomogeneous NLS in Sobolev spaces

Abstract

This work proves the local existence of solutions to some inhomogeneous nonlinear equations of Schrödinger type with a fractional Laplacian in Sobolev spaces. Moreover, for small datum, the local solution extends to a global one. We give an elementary proof based on Strichartz estimates coupled with a fix point argument. In order to avoid a loss of regularity in Strichartz estimates, we consider radial data.