Long time behaviors for the inhomogeneous NLS with a potential in ℝ³

2021/07/13 by Meng, Fanfei, Wang, Sheng, Xu, Chengbin
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2107.06094

Abstract

In this article, we aim to study the scattering of the solution to the focusing inhomogeneous nonlinear Schrödinger equation with a potential of form i∂_t u+Δu- Vu=-|x|^-b|u|^p-1u in the energy space H¹(\R³). We prove a scattering criterion, and then we use it together with Morawetz estimate to show the scattering theory, which generalizes the results of Dinh \citeDD to the non-radial symmetric case.

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