Blowup of cylindrically symmetric solutions for biharmonic NLS
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866913595524120576 |
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| author | Gou, Tianxiang |
| author_facet | Gou, Tianxiang |
| contents | In this paper, we consider blowup of solutions to the Cauchy problem for the following biharmonic nonlinear Schrödinger equation (NLS), $$ \textnormal{i} \, \partial_t u=Δ^2 u-μΔu-|u|^{2 σ} u \quad \text{in} \,\, \R \times \R^d, $$ where $d \geq 1$, $μ\in \R$ and $0<σ<\infty$ if $1 \leq d \leq 4$ and $0<σ<4/(d-4)$ if $d \geq 5$. In the mass critical and supercritical cases, we establish the existence of blowup solutions to the problem for cylindrically symmetric data. The result extends the known ones with respect to blowup of solutions to the problem for radially symmetric data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_08167 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Blowup of cylindrically symmetric solutions for biharmonic NLS Gou, Tianxiang Analysis of PDEs Primary: 35Q55, Secondary: 35B35, 35B44 In this paper, we consider blowup of solutions to the Cauchy problem for the following biharmonic nonlinear Schrödinger equation (NLS), $$ \textnormal{i} \, \partial_t u=Δ^2 u-μΔu-|u|^{2 σ} u \quad \text{in} \,\, \R \times \R^d, $$ where $d \geq 1$, $μ\in \R$ and $0<σ<\infty$ if $1 \leq d \leq 4$ and $0<σ<4/(d-4)$ if $d \geq 5$. In the mass critical and supercritical cases, we establish the existence of blowup solutions to the problem for cylindrically symmetric data. The result extends the known ones with respect to blowup of solutions to the problem for radially symmetric data. |
| title | Blowup of cylindrically symmetric solutions for biharmonic NLS |
| topic | Analysis of PDEs Primary: 35Q55, Secondary: 35B35, 35B44 |
| url | https://arxiv.org/abs/2205.08167 |