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A proof of Onsager's Conjecture for the SQG equation

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arxiv 2407.02578 v3 pith:CIP632AQ submitted 2024-07-02 math.AP math-phmath.MP

classification math.APmath-phmath.MP
keywords conjectureequationhamiltonianonsagerregularityallowableconservationconserve
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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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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Unstable vortices, sharp non-uniqueness with forcing, and global smooth solutions for the SQG equation

    math.AP 2025-02 conditional novelty 8.0 of 10

    Non-uniqueness with forcing for alpha-SQG is established across the full supercritical Sobolev range s < alpha + 2/p, using new smooth compactly supported unstable vortices.

  2. 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.

  3. Strong ill-posedness and non-existence in Sobolev spaces for generalized-SQG

    math.AP 2025-02 accept novelty 6.0 of 10

    For generalized SQG with gamma in (-1,1), the paper proves strong ill-posedness and instantaneous non-existence in H^beta for beta in [1,2+gamma) intersect (3/2+gamma,2+gamma).

  4. An Onsager type theorem for the Euler-Boussinesq equations in two spatial dimensions

    math.AP 2025-02 conditional novelty 6.0 of 10

    For every γ<1/3, there exist compactly supported weak solutions (v,θ) to the 2D Euler-Boussinesq system in C^γ(R×T^2) × C^γ(R×T^2) that violate conservation of the temperature's L^p-norm.

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