On well posedness for the inhomogeneous nonlinear Schrödinger equation

2016/06/08 by Guzmán, Carlos M. · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1606.02777

Abstract

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

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