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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

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

Permalink : https://doi.org/10.14943/84174

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アクセス権
open access
DOI
https://doi.org/10.14943/84174
URI
https://hdl.handle.net/2115/69833
タイトル
ON THE STATIONARY NAVIER-STOKES FLOW WITH ISOTROPIC STREAMLINES IN ALL LATITUDES ON A SPHERE OR A 2D HYPERBOLIC SPACE
著者
著者名
Chan, Chi Hin
著者名
Yoneda, Tsuyoshi
言語
英語
キーワード
Navier-Stokes equation
Riemannian manifold
streamlines
発行日
2013-02-28
出版者
Department of Mathematics, Hokkaido University
収録物名
Hokkaido University Preprint Series in Mathematics
巻(号)
1030
ページ
1-43
抄録
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.
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