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

Michele Coti Zelati; Piotr Kalita

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

Analysis of PDEs 2015-12-29 v1

Authors: Michele Coti Zelati , Piotr Kalita

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 H\"older norms, which complement the existing estimates based on commutator analysis.

Keywords

surface quasi-geostrophic equation critical dissipation weak solution global attractor set-valued dynamical system Sobolev regularity Hölder norm

Cite

@article{arxiv.1512.08418,
  title  = {Smooth attractors for weak solutions of the SQG equation with critical dissipation},
  author = {Michele Coti Zelati and Piotr Kalita},
  journal= {arXiv preprint arXiv:1512.08418},
  year   = {2015}
}

Comments

15 pages

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