標題: On the stationary Navier-Stokes flow with isotropic streamlines in all latitudes on a sphere or a 2D hyperbolic space
作者: Chan, Chi Hin
Yoneda, Tsuyoshi
應用數學系
Department of Applied Mathematics
關鍵字: Navier-Stokes equation;Riemannian manifold;streamlines
公開日期: 1-九月-2013
摘要: In this paper, we show the existence of real-analytic stationary Navier-Stokes flows with isotropic streamlines in all latitudes in some simply-connected 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.
URI: http://dx.doi.org/10.4310/DPDE.2013.v10.n3.a1
http://hdl.handle.net/11536/23338
ISSN: 1548-159X
DOI: 10.4310/DPDE.2013.v10.n3.a1
期刊: DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS
Volume: 10
Issue: 3
起始頁: 209
結束頁: 254
顯示於類別:期刊論文