Generic small-scale creation in the two-dimensional Euler equation
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914391284252672 |
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| author | Alazard, Thomas Said, Ayman Rimah |
| author_facet | Alazard, Thomas Said, Ayman Rimah |
| contents | The Cauchy problem for the two-dimensional incompressible Euler equation is globally well-posed for smooth initial data. In this paper, we show that for a dense $G_δ$ set of initial data, the solutions lose regularity in infinite time, thereby confirming a long-standing conjecture of Yudovich in the smooth setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_13079 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Generic small-scale creation in the two-dimensional Euler equation Alazard, Thomas Said, Ayman Rimah Analysis of PDEs The Cauchy problem for the two-dimensional incompressible Euler equation is globally well-posed for smooth initial data. In this paper, we show that for a dense $G_δ$ set of initial data, the solutions lose regularity in infinite time, thereby confirming a long-standing conjecture of Yudovich in the smooth setting. |
| title | Generic small-scale creation in the two-dimensional Euler equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2603.13079 |