Navier–Stokes equations on Riemannian manifolds
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...
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| Vydané v: | Journal of geometry and physics Ročník 148; s. 103543 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
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Elsevier B.V
01.02.2020
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| ISSN: | 0393-0440, 1879-1662 |
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| Abstract | 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. |
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| AbstractList | 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. |
| ArticleNumber | 103543 |
| Author | Tuomela, Jukka Samavaki, Maryam |
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| Cites_doi | 10.2307/1970699 10.4007/annals.2019.189.1.3 10.1016/j.geomphys.2017.07.015 10.1016/S1570-8659(03)09003-3 10.1137/140971798 10.1007/PL00001493 10.1007/s12220-016-9691-1 10.1016/j.geomphys.2016.06.009 10.1007/s10665-007-9167-1 10.1215/ijm/1256044750 |
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