Incompressible 2D Euler equations with non-decaying random initial vorticity
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| author | Iyer, Gautam Filho, Milton C. Lopes Lopes, Helena J. Nussenzveig |
| author_facet | Iyer, Gautam Filho, Milton C. Lopes Lopes, Helena J. Nussenzveig |
| contents | Consider a random initial vorticity $ω_0(x) = \sum_{n\in \mathbb{Z}^2} a_n ϕ(x-n)$, where $ϕ$ is bounded and compactly supported and $\{a_n\}$ are independent, uniformly bounded, mean $0$, variance $1$ random variables (i.e. $ω_0$ is an array of randomly weighted vortex blobs). We prove global well-posedness of weak solutions to the Euler equations in $\mathbf{R}^2$ for almost every such initial vorticity. The main contribution of our work is the construction of a corresponding initial velocity field that grows slowly at infinity, which enables us to apply a recent well-posedness result of Cobb and Koch. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_07096 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Incompressible 2D Euler equations with non-decaying random initial vorticity Iyer, Gautam Filho, Milton C. Lopes Lopes, Helena J. Nussenzveig Analysis of PDEs 76B47 (Primary) 76B03, 76F99 (Secondary) Consider a random initial vorticity $ω_0(x) = \sum_{n\in \mathbb{Z}^2} a_n ϕ(x-n)$, where $ϕ$ is bounded and compactly supported and $\{a_n\}$ are independent, uniformly bounded, mean $0$, variance $1$ random variables (i.e. $ω_0$ is an array of randomly weighted vortex blobs). We prove global well-posedness of weak solutions to the Euler equations in $\mathbf{R}^2$ for almost every such initial vorticity. The main contribution of our work is the construction of a corresponding initial velocity field that grows slowly at infinity, which enables us to apply a recent well-posedness result of Cobb and Koch. |
| title | Incompressible 2D Euler equations with non-decaying random initial vorticity |
| topic | Analysis of PDEs 76B47 (Primary) 76B03, 76F99 (Secondary) |
| url | https://arxiv.org/abs/2512.07096 |