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Hokkaido University Preprint Series in Mathematics >
ON THE STATIONARY NAVIER-STOKES FLOW WITH ISOTROPIC STREAMLINES IN ALL LATITUDES ON A SPHERE OR A 2D HYPERBOLIC SPACE
| Title: | ON THE STATIONARY NAVIER-STOKES FLOW WITH ISOTROPIC STREAMLINES IN ALL LATITUDES ON A SPHERE OR A 2D HYPERBOLIC SPACE |
| Authors: | Chan, Chi Hin Browse this author | | Yoneda, Tsuyoshi Browse this author |
| Keywords: | Navier-Stokes equation | | Riemannian manifold | | streamlines |
| Issue Date: | 28-Feb-2013 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 1030 |
| Start Page: | 1 |
| End Page: | 43 |
| 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. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69833 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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