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

Fanfei Meng; Sheng Wang; Chengbin Xu

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

Analysis of PDEs 2024-01-05 v5

Authors: Fanfei Meng , Sheng Wang , Chengbin Xu

Abstract

In this article, we aim to study the scattering of the solution to the focusing inhomogeneous nonlinear Schr\"odinger equation with a potential of form \begin{align*} i\partial_t u+\Delta u- Vu=-|x|^{-b}|u|^{p-1}u \end{align*} in the energy space $H^1(\R^3)$ . 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.

Keywords

nonlinear schrödinger equation scattering potential morawetz estimate energy space non-radial case

Cite

@article{arxiv.2107.06094,
  title  = {Long time behaviors for the inhomogeneous NLS with a potential in $\mathbb{R}^3$},
  author = {Fanfei Meng and Sheng Wang and Chengbin Xu},
  journal= {arXiv preprint arXiv:2107.06094},
  year   = {2024}
}

Comments

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

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