A Stochastic RAGE Theorem and Enhanced Dissipation for Transport Noise
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909690112245760 |
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| author | Zelati, Michele Coti Hairer, Martin Villringer, David |
| author_facet | Zelati, Michele Coti Hairer, Martin Villringer, David |
| contents | We prove a stochastic version of the classical RAGE theorem that applies to the two-point motion generated by noisy transport equations. As a consequence, we identify a necessary and sufficient condition for the corresponding diffusive equation to be dissipation enhancing. This involves the identification of a non-trivial, finite dimensional subspace that is invariant for the family of self-adjoint operator characterizing the structure of the transport noise. We discuss several examples and prove a sharp enhanced dissipation rate for stochastic shear flows. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_11422 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Stochastic RAGE Theorem and Enhanced Dissipation for Transport Noise Zelati, Michele Coti Hairer, Martin Villringer, David Analysis of PDEs Probability 60H15, 35Q35, 35R60 We prove a stochastic version of the classical RAGE theorem that applies to the two-point motion generated by noisy transport equations. As a consequence, we identify a necessary and sufficient condition for the corresponding diffusive equation to be dissipation enhancing. This involves the identification of a non-trivial, finite dimensional subspace that is invariant for the family of self-adjoint operator characterizing the structure of the transport noise. We discuss several examples and prove a sharp enhanced dissipation rate for stochastic shear flows. |
| title | A Stochastic RAGE Theorem and Enhanced Dissipation for Transport Noise |
| topic | Analysis of PDEs Probability 60H15, 35Q35, 35R60 |
| url | https://arxiv.org/abs/2507.11422 |