On the pathwise uniqueness of stochastic 2D Euler equations with Kraichnan noise and $L^p$-data
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909221596954624 |
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| author | Jiao, Shuaijie Luo, Dejun |
| author_facet | Jiao, Shuaijie Luo, Dejun |
| contents | In the recent work [arXiv:2308.03216], Coghi and Maurelli proved pathwise uniqueness of solutions to the vorticity form of stochastic 2D Euler equation, with Kraichnan transport noise and initial data in $L^1\cap L^p$ for $p>3/2$. The aim of this note is to remove the constraint on $p$, showing that pathwise uniqueness holds for all $L^1\cap L^p$ initial data with arbitrary $p>1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_07167 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the pathwise uniqueness of stochastic 2D Euler equations with Kraichnan noise and $L^p$-data Jiao, Shuaijie Luo, Dejun Probability In the recent work [arXiv:2308.03216], Coghi and Maurelli proved pathwise uniqueness of solutions to the vorticity form of stochastic 2D Euler equation, with Kraichnan transport noise and initial data in $L^1\cap L^p$ for $p>3/2$. The aim of this note is to remove the constraint on $p$, showing that pathwise uniqueness holds for all $L^1\cap L^p$ initial data with arbitrary $p>1$. |
| title | On the pathwise uniqueness of stochastic 2D Euler equations with Kraichnan noise and $L^p$-data |
| topic | Probability |
| url | https://arxiv.org/abs/2406.07167 |