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Non-unique weak solutions of forced SQG

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arxiv 2310.13537 v1 pith:52CJLPVV submitted 2023-10-20 math.AP

Mimi Dai , Qirui Peng This is my paper · ORCID
classification math.AP
keywords solutionsnon-uniqueweakalphaforcedthetaachievedadapted
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abstract

We construct non-unique weak solutions $\theta\in C_t^0C_x^{0-}$ for forced surface quasi-geostrophic (SQG) equation. This is achieved through a convex integration scheme adapted to the sum-difference system of two distinct solutions. Without external forcing, non-unique weak solutions $\theta$ in space $C_t^0C_x^{\alpha}$ with $\alpha<-\frac15$ were constructed by Buckmaster, Shkoller and Vicol, and Isett and Ma.

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Cited by 2 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. 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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