The dynamics of the focusing NLH with a potential beyond the mass-energy threshold
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909413187518464 |
|---|---|
| author | Ji, Shuang Lu, Jing Meng, Fanfei |
| author_facet | Ji, Shuang Lu, Jing Meng, Fanfei |
| contents | We study the dynamics of the focusing nonlinear Hartree equation with a Kato potential $$ i\partial_t u +Δu - Vu = -(|\cdot|^{-γ} \ast |u|^2)u, \quad x \in \mathbb{R}^d $$ under some assumptions on the potential $V$. We prove the blow up versus global existence dichotomy for solutions beyond the threshold, based on the method from Duyckaerts-Roudenko [6].
Furthermore, our result compensates for the one of in [13] below that threshold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_02103 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The dynamics of the focusing NLH with a potential beyond the mass-energy threshold Ji, Shuang Lu, Jing Meng, Fanfei Analysis of PDEs We study the dynamics of the focusing nonlinear Hartree equation with a Kato potential $$ i\partial_t u +Δu - Vu = -(|\cdot|^{-γ} \ast |u|^2)u, \quad x \in \mathbb{R}^d $$ under some assumptions on the potential $V$. We prove the blow up versus global existence dichotomy for solutions beyond the threshold, based on the method from Duyckaerts-Roudenko [6]. Furthermore, our result compensates for the one of in [13] below that threshold. |
| title | The dynamics of the focusing NLH with a potential beyond the mass-energy threshold |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2412.02103 |