A Liouville type theorem for axially symmetric D-solutions to steady Navier–Stokes equations. (October 2019)

• Record Type: Journal Article
• Authors: Zhao, Na
• Is Part Of: Nonlinear analysis. Volume 187(2019)
• Page Start: 247
• Page End: 258
• Publication Date: 2019-10
• Subjects: Navier–Stokes equations -- D-solutions -- Liouville theorem; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.04.018
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study axially symmetric D -solutions of three dimensional steady Navier–Stokes equations. We prove that if the velocity u decays like | x ′ | − ( 2 3 ) + uniformly for z, or the vorticity ω decays like | x ′ | − ( 5 3 ) + uniformly for z, then u vanishes. Here | x ′ | denotes the distance to the axis.