Abstract:We consider the critical dissipative surface quasi-geostrophic (SQG) equation on $\mathbb{R}^2$ or $\mathbb{T}^2$. Despite global regularity of the equation, we show that the data-to-solution map at the critical level $H^1$ is not uniformly bounded. We construct solutions that experience $H^1$ norm inflation from smooth, compactly supported initial data with large $H^1$ norm. We also demonstrate small-data norm inflation in supercritical Sobolev spaces $W^{\beta,p}$ for $1<p<2$ and $1\le\beta<\tfrac{2}{p}$.
| Comments: | minor revisions, 29 pages |
| Subjects: | Analysis of PDEs (math.AP) |
| Cite as: | arXiv:2512.08816 [math.AP] |
| (or arXiv:2512.08816v2 [math.AP] for this version) | |
| https://doi.org/10.48550/arXiv.2512.08816 arXiv-issued DOI via DataCite |
From: Dengjun Guo [view email]
[v1]
Tue, 9 Dec 2025 17:09:40 UTC (30 KB)
[v2]
Tue, 26 May 2026 12:59:06 UTC (29 KB)
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