Quasi-invariance of the Gaussian measure for the two-dimensional stochastic cubic nonlinear wave equation
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929521918214144 |
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| author | Forlano, Justin Tolomeo, Leonardo |
| author_facet | Forlano, Justin Tolomeo, Leonardo |
| contents | We consider the stochastic damped nonlinear wave equation $\partial_t^{2}u+\partial_t u+u-Δu +u^{3} = \sqrt{2} {\langle{\nabla}\rangle^{-s}} ξ$ on the two-dimensional torus $\mathbb T^2$, where $ξ$ denotes a space-time white noise and $s>0$. We show that the measure $\vecμ_s$ corresponding to the unique invariant measure for the flow of the associated linear equation is quasi-invariant under the nonlinear stochastic flow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_20451 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quasi-invariance of the Gaussian measure for the two-dimensional stochastic cubic nonlinear wave equation Forlano, Justin Tolomeo, Leonardo Probability Analysis of PDEs 35L15, 60H15 We consider the stochastic damped nonlinear wave equation $\partial_t^{2}u+\partial_t u+u-Δu +u^{3} = \sqrt{2} {\langle{\nabla}\rangle^{-s}} ξ$ on the two-dimensional torus $\mathbb T^2$, where $ξ$ denotes a space-time white noise and $s>0$. We show that the measure $\vecμ_s$ corresponding to the unique invariant measure for the flow of the associated linear equation is quasi-invariant under the nonlinear stochastic flow. |
| title | Quasi-invariance of the Gaussian measure for the two-dimensional stochastic cubic nonlinear wave equation |
| topic | Probability Analysis of PDEs 35L15, 60H15 |
| url | https://arxiv.org/abs/2409.20451 |