A spatially localized L log L estimate on the vorticity in the 3D NSE

2013/09/10 by Zachary Bradshaw, Z. Bradshaw, Bradshaw, Z. +3 · 1 citation
Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stochastic processes and financial applications #math.AP

paper · pdf · doi:10.48550/arxiv.1309.2519

final version; to appear in IUMJ

openalex publication_date 2013/09/10 · arxiv created 2014/02/07 · arxiv updated 2014/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The purpose of this note is to present a spatially localized L log L bound on the vorticity in the 3D Navier-Stokes equations, assuming a very mild, purely geometric condition. This yields an extra-log decay of the distribution function of the vorticity, which in turn implies breaking the criticality in a physically, numerically, and mathematical analysis-motivated blow-up scenario based on vortex stretching and anisotropic diffusion.

Citations

• Harmonic analysis on nilpotent groups and singular integrals I. Oscillatory integrals
• Hp spaces of several variables

Cited by

• On taming Moffatt-Kimura vortices of doom in the viscous case

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