Well-Posedness for the Euler Equations in Function Spaces of Generalized Smoothness
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909822814781440 |
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| author | Harrison, Nicholas Radke, Zachary |
| author_facet | Harrison, Nicholas Radke, Zachary |
| contents | We consider the question of well-posedness for the incompressible Euler equations in generalized function spaces of the type $B^{s,ψ}_{p,q}(\mathbb{R}^d)$ and $F^{s,ψ}_{p,q}(\mathbb{R}^d)$ where $ψ$ is a slowly varying function in the Karamata sense and $s=d/p+1$. We prove that if $ψ$ grows fast enough, then there is a local in time solution to the Euler equations. We also establish a BKM-type criterion that allows us to obtain global existence in two dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02626 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Well-Posedness for the Euler Equations in Function Spaces of Generalized Smoothness Harrison, Nicholas Radke, Zachary Analysis of PDEs We consider the question of well-posedness for the incompressible Euler equations in generalized function spaces of the type $B^{s,ψ}_{p,q}(\mathbb{R}^d)$ and $F^{s,ψ}_{p,q}(\mathbb{R}^d)$ where $ψ$ is a slowly varying function in the Karamata sense and $s=d/p+1$. We prove that if $ψ$ grows fast enough, then there is a local in time solution to the Euler equations. We also establish a BKM-type criterion that allows us to obtain global existence in two dimensions. |
| title | Well-Posedness for the Euler Equations in Function Spaces of Generalized Smoothness |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2510.02626 |