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arXiv · 2603.11301

Self-similar blow-up profile for the one-dimensional reduction of generalized SQG with infinite energy

Thomas Y. Hou·Xiang Qin·Yannick Sire·Yantao Wu
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Abstract

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.

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Thomas Y. Hou, Xiang Qin, Yannick Sire, Yantao Wu. 2026-03-11. Self-similar blow-up profile for the one-dimensional reduction of generalized SQG with infinite energy. https://arxiv.org/abs/2603.11301

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