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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2107.06094 |
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| _version_ | 1866911747740270592 |
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| author | Meng, Fanfei Wang, Sheng Xu, Chengbin |
| author_facet | Meng, Fanfei Wang, Sheng Xu, Chengbin |
| contents | 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 $H^1(\R^3)$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_06094 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Long time behaviors for the inhomogeneous NLS with a potential in $\mathbb{R}^3$ Meng, Fanfei Wang, Sheng Xu, Chengbin Analysis of PDEs 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 $H^1(\R^3)$. 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. |
| title | Long time behaviors for the inhomogeneous NLS with a potential in $\mathbb{R}^3$ |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2107.06094 |