A sufficient condition of regularity for axially symmetric solutions to the Navier-Stokes equations

2007/02/23 by Grigory Seregin, Wojciech M. Zajączkowski, Seregin, Grigory +1
Engineering · Mathematics · #35K #76D #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.math/0702720

openalex publication_date 2007/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the present paper, we prove a sufficient condition of local regularity for suitable weak solutions to the Navier-Stokes equations having axial symmetry. Our condition is an axially symmetric analog of the so-called L_3,∞-case in the general local regularity theory.

Related

• Local Regularity of Axisymmetric Solutions to the Navier-Stokes Equations
• Regularity Criterion to the axially symmetric Navier-Stokes Equations
• Remarks on Interior Regularity Criterion for an Axially Symmetric Suitable Weak Solution to the Navier Stokes Equations
• On Type I singularities of the local axi-symmetric solutions of the Navier-Stokes equations
• Remarks on local regularity of axisymmetric solutions to the 3D Navier--Stokes equations