Blow-up of cylindrically symmetric solutions for Fractional NLS
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929412511891456 |
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| author | Gou, Tianxiang Radulescu, Vicentiu D. Zhang, Zhitao |
| author_facet | Gou, Tianxiang Radulescu, Vicentiu D. Zhang, Zhitao |
| contents | In this paper, we consider blow-up of solutions to the Cauchy problem for the following fractional NLS, $$ \textnormal{i} \, \partial_t u=(-Δ)^s u-|u|^{2 σ} u \quad \text{in} \,\, \R \times \R^N, $$ where $N \geq 2$, $1/2 <s<1$ and $0<σ<2s/(N-2s)$. In the mass critical and supercritical cases, we establish a criterion for blow-up of solutions to the problem for cylindrically symmetric data. The results extend the known ones with respect to blow-up of solutions to the problem for radially symmetric data in \cite{BHL}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_03842 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Blow-up of cylindrically symmetric solutions for Fractional NLS Gou, Tianxiang Radulescu, Vicentiu D. Zhang, Zhitao Analysis of PDEs 35R11, 35B44 In this paper, we consider blow-up of solutions to the Cauchy problem for the following fractional NLS, $$ \textnormal{i} \, \partial_t u=(-Δ)^s u-|u|^{2 σ} u \quad \text{in} \,\, \R \times \R^N, $$ where $N \geq 2$, $1/2 <s<1$ and $0<σ<2s/(N-2s)$. In the mass critical and supercritical cases, we establish a criterion for blow-up of solutions to the problem for cylindrically symmetric data. The results extend the known ones with respect to blow-up of solutions to the problem for radially symmetric data in \cite{BHL}. |
| title | Blow-up of cylindrically symmetric solutions for Fractional NLS |
| topic | Analysis of PDEs 35R11, 35B44 |
| url | https://arxiv.org/abs/2406.03842 |