On the stationary Navier-Stokes flow with isotropic streamlines in all latitudes on a sphere or a 2D hyperbolic space

Chi-Hin Chan, Tsuyoshi Yoneda

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

In this paper, we show the existence of real-analytic stationary Navier-Stokes flows with isotropic streamlines in all latitudes in some simplyconnected flow region on a rotating round sphere. We also exclude the possibility of having a Poiseuille's flow profile to be one of these stationary Navier- Stokes flows with isotropic streamlines. When the sphere is replaced by a 2-dimensional hyperbolic space, we also give the analog existence result for stationary parallel laminar Navier-Stokes flows along a circular-arc boundary portion of some compact obstacle in the 2-D hyperbolic space. The existence of stationary parallel laminar Navier-Stokes flows along a straight boundary of some obstacle in the 2-D hyperbolic space is also studied. In any one of these cases, we show that a parallel laminar flow with a Poiseuille's flow profile ceases to be a stationary Navier-Stokes flow, due to the curvature of the background manifold.

Original languageEnglish
Pages (from-to)209-254
Number of pages46
JournalDynamics of Partial Differential Equations
Volume10
Issue number3
DOIs
StatePublished - 22 Oct 2013

Keywords

  • Navier-stokes equation
  • Riemannian manifold
  • Streamlines

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