A geometric characterization of potential Navier-Stokes singularities

2025/01/15 by Zhen Lei, Xiao Ren, Lei, Zhen +3 · 1 citation
Engineering · Physics and Astronomy · #Analysis of PDEs (math.AP) #Elasticity and Wave Propagation #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2501.08976

openalex publication_date 2025/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a local suitable weak solution to the Navier-Stokes equations, we prove that if the vorticity vectors belong to a double cone in regions of high vorticity magnitude, then the solution is regular. Roughly speaking this implies that, near a potential singularity, the directions of vorticity cannot avoid any great circle on the unit sphere. Our method, based on the control of local vorticity fluxes, is inspired by the classical Kelvin-Helmholtz law for ideal fluids and the Type I regularity theory for axisymmetric Navier-Stokes solutions.

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• On the Regularity of Navier-Stokes Equations in Critical Space

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