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

2015/12/28 by Michele Coti Zelati, Zelati, Michele Coti, Piotr Kalita +1
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems #Stability and Controllability of Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1512.08418

15 pages

arxiv created 2015/12/28 · openalex publication_date 2015/12/28 · arxiv updated 2015/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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