Navier-Stokes equations on Riemannian manifolds

被引：21

作者：

Samavaki, Maryam ^{[1
]}

Tuomela, Jukka ^{[1
]}

机构：

[1] Univ Eastern Finland, Dept Phys & Math, POB 111, FI-80101 Joensuu, Finland

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2020年 / 148卷

关键词：

Curvature tensor; Killing vector fields; Navier-Stokes equations; Riemannian manifolds;

D O I：

10.1016/j.geomphys.2019.103543

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study properties of the solutions to Navier-Stokes system on compact Riemannian manifolds. The motivation for such a formulation comes from atmospheric models as well as some thin film flows on curved surfaces. There are different choices of the diffusion operator which have been used in previous studies, and we make a few comments why the choice adopted below seems to us the correct one. This choice leads to the conclusion that Killing vector fields are essential in analyzing the qualitative properties of the flow. We give several results illustrating this and analyze also the linearized version of Navier-Stokes system which is interesting in numerical applications. Finally we consider the 2 dimensional case which has specific characteristics, and treat also the Coriolis effect which is essential in atmospheric flows. (C) 2019 Elsevier B.V. All rights reserved.

引用

页数：15

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