On the stationary Navier–Stokes problem in 3D exterior domains. Issue 9 (3rd July 2020)

• Record Type: Journal Article
• Authors: Coscia, Vincenzo; Russo, Remigio; Tartaglione, Alfonsina
• Is Part Of: Applicable analysis. Volume 99:Issue 9(2020)
• Page Start: 1485
• Page End: 1506
• Publication Date: 2020-07-03
• Subjects: Stationary Stokes and Navier–Stokes equations -- three-dimensional exterior domains -- boundary value problems; Primary: 76D05, 35Q30 -- Secondary: 31B10, 76D03; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1538502
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: The main purpose of this paper is to show that in a three-dimensional exterior Lipschitz domain Ω = R 3 ∖ ∪ i = 1 m Ω ¯ i the stationary Navier–Stokes equations have a solution which converges at infinity to a constant vector and assumes a boundary value a ∈ L 2 ( ∂Ω ) (or a ∈ W − 1 / 3, 3 ( ∂Ω ) if Ω is of class C 1, 1 ), provided ∑ i = 1 m | ∫ ∂ Ω i a ⋅ n | max ξ ∈ ∂ Ω i ( 1 / | ξ − x i | ) < 8 π ν . Moreover, for large value of the viscosity ν we prove existence, uniqueness and asymptotics of a solution u ∈ L 3 ( Ω ) for Ω and a polar symmetric.