Local well-posedness of subcritical non-linear heat equations with Gaussian initial data
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913998853636096 |
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| author | Chevyrev, Ilya Mirsajjadi, Hora |
| author_facet | Chevyrev, Ilya Mirsajjadi, Hora |
| contents | We show that any non-linear heat equation with scaling critical dimension $-1$ is locally well-posed when its initial condition is taken as the Gaussian free field in fractional dimension $d < 4$. Our results in particular extend the well-posedness results of arXiv:2111.10652, arXiv:2201.03487 from $d=3$ to the entire subcritical regime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_11638 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local well-posedness of subcritical non-linear heat equations with Gaussian initial data Chevyrev, Ilya Mirsajjadi, Hora Probability Analysis of PDEs 35R60, 60G15 (Primary) 35A01, 81T18 (Secondary) We show that any non-linear heat equation with scaling critical dimension $-1$ is locally well-posed when its initial condition is taken as the Gaussian free field in fractional dimension $d < 4$. Our results in particular extend the well-posedness results of arXiv:2111.10652, arXiv:2201.03487 from $d=3$ to the entire subcritical regime. |
| title | Local well-posedness of subcritical non-linear heat equations with Gaussian initial data |
| topic | Probability Analysis of PDEs 35R60, 60G15 (Primary) 35A01, 81T18 (Secondary) |
| url | https://arxiv.org/abs/2410.11638 |