On the asymptotic behaviour of 2D stationary Navier–Stokes solutions with symmetry conditions. (18th September 2017)

• Record Type: Journal Article
• Authors: Decaster, Agathe; Iftimie, Dragoş
• Is Part Of: Nonlinearity. Volume 30:Number 10(2017:Oct.)
• Page Start: 3951
• Page End: 3978
• Publication Date: 2017-09-18
• Subjects: Navier–Stokes equations -- stationary solutions -- asymptotic behaviour; 35Q35; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aa83a7
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We consider the 2D stationary incompressible Navier-Stokes equations in ℝ 2 . Under suitable symmetry, smallness and decay at infinity conditions on the forcing we determine the behaviour at infinity of the solutions. Moreover, when the forcing is small, satisfies suitable symmetry conditions and decays at infinity like a vector field homogeneous of degree -3, we show that there exists a unique small solution whose asymptotic behaviour at infinity is homogeneous of degree -1.