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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2510.12221 |
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| _version_ | 1866908591794946048 |
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| author | Li, Xue-Mei Ren, Xianfeng |
| author_facet | Li, Xue-Mei Ren, Xianfeng |
| contents | We study the singular stochastic wave equation on $\mathbb T^2$, with a cubic nonlinearity and Gaussian rough Matérn forcing (a Fourier multiplier of order $α>0$ applied to space-time white noise) and establish local well-posedness for $α< \tfrac{3}{8}$. This extends [GKO18] beyond white noise and strengthens the quadratic-case result [OO21] ($α<\tfrac 12$). Our argument develops new trilinear estimates in Bourgain spaces together with sharp, case-specific cubic counting estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_12221 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stochastic nonlinear wave equation with rougher than white noise Li, Xue-Mei Ren, Xianfeng Probability We study the singular stochastic wave equation on $\mathbb T^2$, with a cubic nonlinearity and Gaussian rough Matérn forcing (a Fourier multiplier of order $α>0$ applied to space-time white noise) and establish local well-posedness for $α< \tfrac{3}{8}$. This extends [GKO18] beyond white noise and strengthens the quadratic-case result [OO21] ($α<\tfrac 12$). Our argument develops new trilinear estimates in Bourgain spaces together with sharp, case-specific cubic counting estimates. |
| title | Stochastic nonlinear wave equation with rougher than white noise |
| topic | Probability |
| url | https://arxiv.org/abs/2510.12221 |