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Wellposedness and singularity formation beyond the Yudovich class

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arxiv 2312.17610 v1 pith:NZCXVGOV submitted 2023-12-29 math.AP

Tarek M. Elgindi , Ryan W. Murray , Ayman R. Said This is my paper · ORCID
classification math.AP
keywords solutionsclassbeyondeulerfinitesingularitytimewellposedness
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We introduce a local-in-time existence and uniqueness class for solutions to the 2d Euler equation with unbounded vorticity. Furthermore, we show that solutions belonging to this class can develop stronger singularities in finite time, meaning that they experience finite time blow up and exit the wellposedness class. Such solutions may be continued as weak solutions (potentially non-uniquely) after the singularity. While the general dynamics of 2d Euler solutions beyond the Yudovich class will certainly not be so tame, studying such solutions gives a way to study singular phenomena in a more controlled setting.

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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. Pathological solutions of Navier-Stokes equations on $\mathbb{T}^2$ with gradients in Hardy spaces

    math.AP 2025-09 conditional novelty 7.0 of 10

    For 2D Navier-Stokes on a torus, non-uniqueness holds with velocity gradients in C([0,T], H^p) for every exponent 0 < p < 1, making p = 1 the sharp threshold between non-uniqueness and uniqueness in the vorticity path space.

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