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| Main Authors: | , |
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| Format: | Preprint |
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2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.14813 |
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| _version_ | 1866914269391486976 |
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| author | Schindler, Jule Wiedemann, Emil |
| author_facet | Schindler, Jule Wiedemann, Emil |
| contents | We consider the inviscid Leray-$α$ equations - an inviscid nonlocal regularisation of the Euler equations. In the first part, we prove the convergence of strong solutions of the Leray-$α$ equations to strong solutions of the Euler equations in $H^s(\mathbb{R}^d)$ for $s>d/2 +1 $, $d\in \{2,3\}$, for a large class of regularising kernels. In the second part, we consider weak solutions on a bounded domain with a local scaling property far away from the boundary. The scaling relates to second-order structure functions from turbulence theory and does not imply regularity. Nonetheless, under these assumptions, the weak solutions converge to (possibly wild) weak solutions of Euler in $L^2$ for almost every $t$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_14813 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Nonlocal-to-Local Limit for the Inviscid Leray-α Equations Schindler, Jule Wiedemann, Emil Analysis of PDEs We consider the inviscid Leray-$α$ equations - an inviscid nonlocal regularisation of the Euler equations. In the first part, we prove the convergence of strong solutions of the Leray-$α$ equations to strong solutions of the Euler equations in $H^s(\mathbb{R}^d)$ for $s>d/2 +1 $, $d\in \{2,3\}$, for a large class of regularising kernels. In the second part, we consider weak solutions on a bounded domain with a local scaling property far away from the boundary. The scaling relates to second-order structure functions from turbulence theory and does not imply regularity. Nonetheless, under these assumptions, the weak solutions converge to (possibly wild) weak solutions of Euler in $L^2$ for almost every $t$. |
| title | The Nonlocal-to-Local Limit for the Inviscid Leray-α Equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2601.14813 |