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arXiv · 1506.06375

Uniformly attracting limit sets for the critically dissipative SQG equation

Peter Constantin·Michele Coti Zelati·Vlad Vicol
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Abstract

We consider the global attractor of the critical SQG semigroup $S(t)$ on the scale-invariant space $H^1(\mathbb{T}^2)$. It was shown in~\cite{CTV13} that this attractor is finite dimensional, and that it attracts uniformly bounded sets in $H^{1+δ}(\mathbb{T}^2)$ for any $δ>0$, leaving open the question of uniform attraction in $H^1(\mathbb{T}^2)$. In this paper we prove the uniform attraction in $H^1(\mathbb{T}^2)$, by combining ideas from DeGiorgi iteration and nonlinear maximum principles.

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Peter Constantin, Michele Coti Zelati, Vlad Vicol. 2015-06-21. Uniformly attracting limit sets for the critically dissipative SQG equation. https://doi.org/10.1088/0951-7715%2F29%2F2%2F298

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