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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.05599 |
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| _version_ | 1866908513295400960 |
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| author | Vu, Xuan-Truong |
| author_facet | Vu, Xuan-Truong |
| contents | In this paper, we study the logarithmically regularized $2$D Euler system \eqref{e1}, which is derived by regularizing the Euler equation for the vorticity. We establish local well-posedness of the logarithmically regularized $2$D Euler equations in the subcritical space $H^s(\mathbb{R}^2)$ with $s>2$ for $γ\ge 0$. Furthermore, we show that for $γ$ close to $0$, the data-to-solution map is not uniformly continuous in the Sobolev $H^s(\mathbb{R}^2)$ topology for any $s>2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_05599 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Instability of Data-to-Solution Map for the Log-Regularized 2D Euler System Vu, Xuan-Truong Analysis of PDEs 35Q31, 35B30 In this paper, we study the logarithmically regularized $2$D Euler system \eqref{e1}, which is derived by regularizing the Euler equation for the vorticity. We establish local well-posedness of the logarithmically regularized $2$D Euler equations in the subcritical space $H^s(\mathbb{R}^2)$ with $s>2$ for $γ\ge 0$. Furthermore, we show that for $γ$ close to $0$, the data-to-solution map is not uniformly continuous in the Sobolev $H^s(\mathbb{R}^2)$ topology for any $s>2$. |
| title | Instability of Data-to-Solution Map for the Log-Regularized 2D Euler System |
| topic | Analysis of PDEs 35Q31, 35B30 |
| url | https://arxiv.org/abs/2410.05599 |