Self-similar blowup from arbitrary data for supercritical wave maps with additive noise
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914121907175424 |
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| author | Glogić, Irfan Hofmanová, Martina Luongo, Eliseo |
| author_facet | Glogić, Irfan Hofmanová, Martina Luongo, Eliseo |
| contents | We consider stochastically perturbed wave maps from $\mathbb{R}^{1+d}$ into $\mathbb{S}^d$, in all energy-supercritical dimensions $d \geq 3$. We show that corotational non-degenerate Gaussian additive noise leads to self-similar blowup with positive probability for any corotational initial data. The same result without noise is conjectured, but unknown, for large data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_25326 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Self-similar blowup from arbitrary data for supercritical wave maps with additive noise Glogić, Irfan Hofmanová, Martina Luongo, Eliseo Analysis of PDEs Mathematical Physics Differential Geometry Probability We consider stochastically perturbed wave maps from $\mathbb{R}^{1+d}$ into $\mathbb{S}^d$, in all energy-supercritical dimensions $d \geq 3$. We show that corotational non-degenerate Gaussian additive noise leads to self-similar blowup with positive probability for any corotational initial data. The same result without noise is conjectured, but unknown, for large data. |
| title | Self-similar blowup from arbitrary data for supercritical wave maps with additive noise |
| topic | Analysis of PDEs Mathematical Physics Differential Geometry Probability |
| url | https://arxiv.org/abs/2510.25326 |