Dynamics of Partial Differential Equations

Volume 14 (2017)

Number 3

Asymptotic behavior of the steady Navier–Stokes equation on the hyperbolic plane

Pages: 239 – 270

DOI: https://dx.doi.org/10.4310/DPDE.2017.v14.n3.a2

Authors

Chi Hin Chan (Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan)

Che-Kai Chen (Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan)

Magdalena Czubak (Department of Mathematics, University of Colorado, Boulder, Co., U.S.A.)

Abstract

We develop the asymptotic behavior for the solutions to the stationary Navier–Stokes equation in the exterior domain of the 2D hyperbolic space. More precisely, given the finite Dirichlet norm of the velocity, we show the velocity decays to $0$ at infinity. We also address the decay rate for the vorticity and the behavior of the pressure.

Keywords

exterior domain, Stationary Navier–Stokes, asymptotics, hyperbolic plane

2010 Mathematics Subject Classification

58J05, 76D03, 76D05

Full Text (PDF format)

Received 3 May 2017

Published 8 September 2017