On blow-up for the supercritical defocusing nonlinear wave equation
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866912302747353088 |
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| author | Shao, Feng Wei, Dongyi Zhang, Zhifei |
| author_facet | Shao, Feng Wei, Dongyi Zhang, Zhifei |
| contents | In this paper, we consider the defocusing nonlinear wave equation $-\partial_t^2u+Δu=|u|^{p-1}u$ in $\mathbb R\times \mathbb R^d$. Building on our companion work ({\it \small Self-similar imploding solutions of the relativistic Euler equations}), we prove that for $d=4, p\geq 29$ and $d\geq 5, p\geq 17$, there exists a smooth complex-valued solution that blows up in finite time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19674 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On blow-up for the supercritical defocusing nonlinear wave equation Shao, Feng Wei, Dongyi Zhang, Zhifei Analysis of PDEs In this paper, we consider the defocusing nonlinear wave equation $-\partial_t^2u+Δu=|u|^{p-1}u$ in $\mathbb R\times \mathbb R^d$. Building on our companion work ({\it \small Self-similar imploding solutions of the relativistic Euler equations}), we prove that for $d=4, p\geq 29$ and $d\geq 5, p\geq 17$, there exists a smooth complex-valued solution that blows up in finite time. |
| title | On blow-up for the supercritical defocusing nonlinear wave equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2405.19674 |