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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.11301 |
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| _version_ | 1866915855147728896 |
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| author | Hou, Thomas Y. Qin, Xiang Sire, Yannick Wu, Yantao |
| author_facet | Hou, Thomas Y. Qin, Xiang Sire, Yannick Wu, Yantao |
| contents | We study the singularity formation mechanisms of the inviscid generalized Surface Quasi-Geostrophic (gSQG) equation on the whole space $\mathbb{R}^2$ and on the upper half-plane $\mathbb{R}^2_+$, allowing infinite energy. In each case, we derive a one-dimensional reduction that captures the leading-order singular behavior of the original 2D system, and use a fixed-point argument to show the existence of finite-time self-similar blow-up solutions for the 1D systems. We also perform numerical simulations for verification and visualization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_11301 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Self-similar blow-up profile for the one-dimensional reduction of generalized SQG with infinite energy Hou, Thomas Y. Qin, Xiang Sire, Yannick Wu, Yantao Analysis of PDEs We study the singularity formation mechanisms of the inviscid generalized Surface Quasi-Geostrophic (gSQG) equation on the whole space $\mathbb{R}^2$ and on the upper half-plane $\mathbb{R}^2_+$, allowing infinite energy. In each case, we derive a one-dimensional reduction that captures the leading-order singular behavior of the original 2D system, and use a fixed-point argument to show the existence of finite-time self-similar blow-up solutions for the 1D systems. We also perform numerical simulations for verification and visualization. |
| title | Self-similar blow-up profile for the one-dimensional reduction of generalized SQG with infinite energy |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2603.11301 |