Long time behaviors for the inhomogeneous NLS with a potential in ${\mathbb{R}}^3$

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 \begin{align*} i\partial_t u+Δu- Vu=-|x|^{-b}|u|^{p-1}u \end{align*} in the energy space $H^1({\mathbb{R}}^3)$. 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 \cite{DD} to the non-radial symmetric case.

In this version, we correct some mistakes and change the title

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