ON THE STATIONARY NAVIER-STOKES FLOW WITH ISOTROPIC STREAMLINES IN ALL LATITUDES ON A SPHERE OR A 2D HYPERBOLIC SPACE

• Chan Chi Hin

• Yoneda Tsuyoshi

Abstract

In this paper, we show the existence of real-analytic stationary NavierStokesflows with isotropic streamlines in all latitudes in some simply-connected flow regionon a rotating round sphere. We also exclude the possibility of having a Poiseuille’sflow 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 givethe analog existence result for stationary parallel laminar Navier-Stokes flows along acircular-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 boundaryof some obstacle in the 2-D hyperbolic space is also studied. In any one of thesecases, we show that a parallel laminar flow with a Poiseuille’s flow profile ceases to bea stationary Navier-Stokes flow, due to the curvature of the background manifold.

Journal

• Hokkaido University Preprint Series in Mathematics

  Hokkaido University Preprint Series in Mathematics 1030 1-43, 2013-02-28

  Department of Mathematics, Hokkaido University

Keywords

• Navier-Stokes equation
• Riemannian manifold
• streamlines

Details

• CRID: 1390853649725592192
• NII Article ID: 120006459719
• DOI: 10.14943/84174
• HANDLE: 2115/69833
• Text Lang: en
• Data Source:
  • JaLC
  • IRDB
  • CiNii Articles
• Abstract License Flag: Allowed