Stable blowup for focusing semilinear wave equations in all dimensions
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910436912267264 |
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| author | Ostermann, Matthias |
| author_facet | Ostermann, Matthias |
| contents | We consider the wave equation with focusing power nonlinearity. The associated ODE in time gives rise to a self-similar solution known as the ODE blowup. We prove the nonlinear asymptotic stability of this blowup mechanism outside of radial symmetry in all space dimensions and for all superlinear powers. This result covers for the first time the whole energy-supercritical range without symmetry restrictions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_08187 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stable blowup for focusing semilinear wave equations in all dimensions Ostermann, Matthias Analysis of PDEs Mathematical Physics We consider the wave equation with focusing power nonlinearity. The associated ODE in time gives rise to a self-similar solution known as the ODE blowup. We prove the nonlinear asymptotic stability of this blowup mechanism outside of radial symmetry in all space dimensions and for all superlinear powers. This result covers for the first time the whole energy-supercritical range without symmetry restrictions. |
| title | Stable blowup for focusing semilinear wave equations in all dimensions |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2304.08187 |