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arXiv · 2012.12006

Estimate on the dimension of the singular set of the supercritical surface quasigeostrophic equation

Maria Colombo·Silja Haffter
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Abstract

We consider the SQG equation with dissipation given by a fractional Laplacian of order $\alpha<\frac{1}{2}$. We introduce a notion of suitable weak solution, which exists for every $L^2$ initial datum, and we prove that for such solution the singular set is contained in a compact set in spacetime of Hausdorff dimension at most $\frac{1}{2\alpha} \left( \frac{1+\alpha}{\alpha} (1-2\alpha) + 2\right)$.

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Maria Colombo, Silja Haffter. 2020-12-22. Estimate on the dimension of the singular set of the supercritical surface quasigeostrophic equation. https://arxiv.org/abs/2012.12006

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