A proof of Onsager's Conjecture for the SQG equation

2024/07/02 by Isett, Philip, Looi, Shi-Zhuo · 3 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2407.02578

Abstract

We construct solutions to the SQG equation that fail to conserve the Hamiltonian while having the maximal allowable regularity for this property to hold. This result solves the generalized Onsager conjecture on the threshold regularity for Hamiltonian conservation for SQG.

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• Intermittent solutions of the stationary 2D surface quasi-geostrophic equation
• Stationary homogeneous solutions for the inviscid SQG equation
• Global Existence, Hamiltonian Conservation and Vanishing Viscosity for the Surface Quasi-Geostrophic Equation

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