Norm Inflation For The Critical SQG Equation

Dengjun Guo; Xiaoyutao Luo

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arXiv · 2512.08816

Norm Inflation For The Critical SQG Equation

Dengjun Guo·Xiaoyutao Luo

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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 $1\le\beta<\tfrac{2}{p}$.

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Dengjun Guo, Xiaoyutao Luo. 2025-12-09. Norm Inflation For The Critical SQG Equation. https://arxiv.org/abs/2512.08816

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