Anomalous Regularization in Kazantsev-Kraichnan Model
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913578047504384 |
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| author | Bagnara, Marco Grotto, Francesco Maurelli, Mario |
| author_facet | Bagnara, Marco Grotto, Francesco Maurelli, Mario |
| contents | This work investigates a passive vector field which is transported and stretched by a divergence-free Gaussian velocity field, delta-correlated in time and poorly correlated in space (spatially nonsmooth). Although the advection of a scalar field (Kraichnan's passive scalar model) is known to enjoy regularizing properties, the potentially competing stretching term in vector advection may induce singularity formation. We establish that the regularization effect is actually retained in certain regimes. While this is true in any dimension $d\ge 3$, it notably implies a regularization result for linearized 3D Euler equations with stochastic modeling of turbulent velocities, and for the induction equation in magnetohydrodynamic turbulence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09482 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Anomalous Regularization in Kazantsev-Kraichnan Model Bagnara, Marco Grotto, Francesco Maurelli, Mario Probability Analysis of PDEs 76F55, 76M35, 60H15, 76F25 This work investigates a passive vector field which is transported and stretched by a divergence-free Gaussian velocity field, delta-correlated in time and poorly correlated in space (spatially nonsmooth). Although the advection of a scalar field (Kraichnan's passive scalar model) is known to enjoy regularizing properties, the potentially competing stretching term in vector advection may induce singularity formation. We establish that the regularization effect is actually retained in certain regimes. While this is true in any dimension $d\ge 3$, it notably implies a regularization result for linearized 3D Euler equations with stochastic modeling of turbulent velocities, and for the induction equation in magnetohydrodynamic turbulence. |
| title | Anomalous Regularization in Kazantsev-Kraichnan Model |
| topic | Probability Analysis of PDEs 76F55, 76M35, 60H15, 76F25 |
| url | https://arxiv.org/abs/2411.09482 |