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Non-uniqueness up to the Onsager threshold for the forced SQG equation

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arxiv 2310.12947 v1 pith:6FORI547 submitted 2023-10-19 math.AP

Aynur Bulut , Manh Khang Huynh , Stan Palasek This is my paper
classification math.AP
keywords alphaequationforcednon-uniquenessresultsalternatingclassconvex
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abstract

We establish new non-uniqueness results for the forced inviscid surface quasi-geostrophic equation, via an alternating formulation of convex integration techniques. Our results imply non-uniquenesss in the class of weak solutions with $|\nabla|^{-1}\theta\in C_tC_x^\alpha$, for any $\alpha<1$.

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Cited by 1 Pith paper

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  1. Global Existence, Hamiltonian Conservation and Vanishing Viscosity for the Surface Quasi-Geostrophic Equation

    math.AP 2025-09 accept novelty 7.0 of 10

    For any L^{4/3}_x initial datum there exists a global weak solution of SQG conserving the H^{-1/2}_x Hamiltonian, obtained via a vanishing-viscosity limit with no anomalous dissipation.

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