A Liouville type theorem for axially symmetric D-solutions to steady Navier-Stokes Equations

2018/05/10 by Na Zhao, Zhao, Na
Engineering · Mathematics · #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.1805.03845

openalex publication_date 2018/05/10 · openalex created_date 2018/05/17 · openalex updated_date 2026/07/28

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.

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