No blow-up by nonlinear Itô noise for the Euler equations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913864506933248 |
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| author | Bagnara, Marco Maurelli, Mario Xu, Fanhui |
| author_facet | Bagnara, Marco Maurelli, Mario Xu, Fanhui |
| contents | By employing a suitable multiplicative Itô noise with radial structure and with more than linear growth, we show the existence of a unique, global-in-time, strong solution for the stochastic Euler equations in two and three dimensions. More generally, we consider a class of stochastic partial differential equations (SPDEs) with a superlinear growth drift and suitable nonlinear, multiplicative Itô noise, with the stochastic Euler equations as a special case within this class. We prove that the addition of such a noise effectively prevents blow-ups in the solution of these SPDEs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_09852 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | No blow-up by nonlinear Itô noise for the Euler equations Bagnara, Marco Maurelli, Mario Xu, Fanhui Probability 60H15, 76B03 By employing a suitable multiplicative Itô noise with radial structure and with more than linear growth, we show the existence of a unique, global-in-time, strong solution for the stochastic Euler equations in two and three dimensions. More generally, we consider a class of stochastic partial differential equations (SPDEs) with a superlinear growth drift and suitable nonlinear, multiplicative Itô noise, with the stochastic Euler equations as a special case within this class. We prove that the addition of such a noise effectively prevents blow-ups in the solution of these SPDEs. |
| title | No blow-up by nonlinear Itô noise for the Euler equations |
| topic | Probability 60H15, 76B03 |
| url | https://arxiv.org/abs/2305.09852 |