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Non-unique stationary solutions of forced SQG

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arxiv 2302.03283 v1 pith:FTEFOSH4 submitted 2023-02-07 math.AP

Mimi Dai , Qirui Peng This is my paper · ORCID
classification math.AP
keywords schemesolutionsflexibilityforcedforcingnon-uniquestationarysystem
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We show the existence of non-unique stationary weak solutions for forced surface quasi-geostrophic (SQG) equation via a convex integration scheme. The scheme is implemented for the sum-difference system of two distinct solutions. Through this scheme, one observes the external forcing is naturally generated accompanying the flexibility in means of lack of uniqueness. It thus provides a transparent way to reveal the flexibility of the system with the presence of a forcing.

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Cited by 3 Pith papers

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

  1. Smooth nonradial stationary solutions to SQG via the half-Yamabe equation

    math.AP 2026-08 conditional novelty 7.0 of 10

    Infinitely many smooth nonradial finite-energy stationary SQG solutions are claimed, built from sign-changing k-bubble solutions of (−Δ)^{1/2}ψ = ψ³ concentrated at polygon vertices at scale (k log k)^{−2}.

  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).

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