On well posedness for the inhomogeneous nonlinear Schrödinger equation

Abstract

The purpose of this paper is to study well-posedness of the initial value problem (IVP) for the inhomogeneous nonlinear Schrödinger equation (INLS) iut+Δu+λ|x|−b|u|αu=0,where λ=±1 and α, b>0.We obtain local and global results for initial data in Hs(RN), with 0≤s≤1. To this end, we use the contraction mapping principle based on the Strichartz estimates related to the linear problem.