Path-connectedness of incompressible Euler solutions
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909597001842688 |
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| author | Anjolras, Philippe |
| author_facet | Anjolras, Philippe |
| contents | We study the incompressible Euler equation and prove that the set of weak solutions is path-connected. More precisely, we construct paths of Hölder regularity $C^{1/2}$, valued in $C^0_{t, loc} L^2_x$ endowed with the strong topology. The main result relies on a convex integration construction adapted from the seminal work of De Lellis and Székelyhidi [14, The Euler equations as a differential inclusion], extending it to a more broader geometric framework, replacing balls with arbitrary convex compact sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_20737 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Path-connectedness of incompressible Euler solutions Anjolras, Philippe Analysis of PDEs We study the incompressible Euler equation and prove that the set of weak solutions is path-connected. More precisely, we construct paths of Hölder regularity $C^{1/2}$, valued in $C^0_{t, loc} L^2_x$ endowed with the strong topology. The main result relies on a convex integration construction adapted from the seminal work of De Lellis and Székelyhidi [14, The Euler equations as a differential inclusion], extending it to a more broader geometric framework, replacing balls with arbitrary convex compact sets. |
| title | Path-connectedness of incompressible Euler solutions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2504.20737 |