A suitable nonlinear Stratonovich noise prevents blow-up in the Euler equations and other SPDEs
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866916204126404608 |
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| author | Bagnara, Marco |
| author_facet | Bagnara, Marco |
| contents | We perturb the 3D Euler equations by a particular non-linear Stratonovich noise. We show the existence and uniqueness of a global-in-time (i.e. no blow-up) smooth solution. The result is a corollary of a more general theorem valid in an abstract framework, where the addition of such noise prevents the blow-up possibly induced by a drift with super-linear growth. The result is new with Stratonovich noise. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_10446 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A suitable nonlinear Stratonovich noise prevents blow-up in the Euler equations and other SPDEs Bagnara, Marco Probability 35Q31, 60H15, 60H50, 76B03 We perturb the 3D Euler equations by a particular non-linear Stratonovich noise. We show the existence and uniqueness of a global-in-time (i.e. no blow-up) smooth solution. The result is a corollary of a more general theorem valid in an abstract framework, where the addition of such noise prevents the blow-up possibly induced by a drift with super-linear growth. The result is new with Stratonovich noise. |
| title | A suitable nonlinear Stratonovich noise prevents blow-up in the Euler equations and other SPDEs |
| topic | Probability 35Q31, 60H15, 60H50, 76B03 |
| url | https://arxiv.org/abs/2312.10446 |