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arXiv · 1512.08418

Smooth attractors for weak solutions of the SQG equation with critical dissipation

Michele Coti Zelati·Piotr Kalita
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Abstract

We consider the evolution of weak vanishing viscosity solutions to the critically dissipative surface quasi-geostrophic equation. Due to the possible non-uniqueness of solutions, we rephrase the problem as a set-valued dynamical system and prove the existence of a global attractor of optimal Sobolev regularity. To achieve this, we derive a new Sobolev estimate involving Hölder norms, which complement the existing estimates based on commutator analysis.

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Michele Coti Zelati, Piotr Kalita. 2015-12-28. Smooth attractors for weak solutions of the SQG equation with critical dissipation. https://arxiv.org/abs/1512.08418

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