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Self-similar algebraic spiral vortex sheets of 2-D incompressible Euler equations

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arxiv 2505.03309 v1 pith:AHWX3X6C submitted 2025-05-06 math.AP

Feng Shao , Dongyi Wei , Zhifei Zhang This is my paper · ORCID
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keywords algebraicspiralvortexequationseulerincompressibleintegralself-similar
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This paper provides the first rigorous construction of the self-similar algebraic spiral vortex sheet solutions to the 2-D incompressible Euler equations. These solutions are believed to represent the typical roll-up pattern of vortex sheets after the formation of curvature singularities. The most challenging part of this paper is to handle the Cauchy integral for the algebraic spiral curve, which falls outside the classical theory of singular integral operators.

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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. Desingularization of vortex sheets for the 2D Euler equations

    math.AP 2025-05 accept novelty 8.0 of 10

    Smooth compactly supported vortex layers around any closed analytic curve evolve, in the zero-thickness limit, according to the Birkhoff-Rott equations.

  2. Asymmetric Self-similar Spiral Solutions of 2-D Incomressible Euler Equations

    math.AP 2025-07 conditional novelty 7.0 of 10

    For self-similar exponent mu > 1, any sufficiently small Fourier-weighted perturbation of a radial vortex produces a genuine asymmetric algebraic spiral weak solution of the 2-D Euler equations.

  3. Finite-time self-similar implosion of hollow vortices

    math.AP 2025-06 conditional novelty 7.0 of 10

    Self-similar finite-time implosion is proved for hollow vortices, including desingularization of collapsing point vortex configurations and new m-fold symmetric rotating branches.

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