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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.19214 |
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| _version_ | 1866911892508770304 |
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| author | Buck, Miriam Modena, Stefano |
| author_facet | Buck, Miriam Modena, Stefano |
| contents | In a previous work (arXiv:2306.05948), we constructed by convex integration examples of energy dissipating solutions to the 2D Euler equations on $\mathbb{R}^2$ with vorticity in the real Hardy space $H^p(\mathbb{R}^2)$. In the present paper, we develop tools that significantly improve that result in two ways: Firstly, we achieve vorticities in $H^p(\mathbb{R}^2)$ in the optimal range $p\in (0,1)$ compared to $(2/3,1)$ in our previous work. Secondly, the solutions constructed here possess compact support and in particular preserve linear and angular momenta. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19214 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Compactly supported anomalous weak solutions for 2D Euler equations with vorticity in Hardy spaces Buck, Miriam Modena, Stefano Analysis of PDEs 35Q31 In a previous work (arXiv:2306.05948), we constructed by convex integration examples of energy dissipating solutions to the 2D Euler equations on $\mathbb{R}^2$ with vorticity in the real Hardy space $H^p(\mathbb{R}^2)$. In the present paper, we develop tools that significantly improve that result in two ways: Firstly, we achieve vorticities in $H^p(\mathbb{R}^2)$ in the optimal range $p\in (0,1)$ compared to $(2/3,1)$ in our previous work. Secondly, the solutions constructed here possess compact support and in particular preserve linear and angular momenta. |
| title | Compactly supported anomalous weak solutions for 2D Euler equations with vorticity in Hardy spaces |
| topic | Analysis of PDEs 35Q31 |
| url | https://arxiv.org/abs/2405.19214 |