Relative decay conditions on Liouville type theorem for the steady Navier-Stokes system

2020/03/11 by Dongho Chae, Chae, Dongho
Engineering · Mathematics · #35Q30 #76D03 #76D05 #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.2003.05246

openalex publication_date 2020/03/11 · openalex created_date 2020/05/13 · openalex updated_date 2026/07/28

Abstract

In this paper we prove Liouville type theorem for the stationary Navier-Stokes equations in \Bbb R³ under the assumptions on the relative decays of velocity, pressure and the head pressure. More precisely, we show that any smooth solution (u,p) of the stationary Navier-Stokes equations satisfying u(x) → 0 as |x|→ +∞ and the condition of finite Dirichlet integral ∫_{\Bbb R³} | ∇ u|² dx

Citations

• Liouville theorems for the Navier–Stokes equations and applications

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