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Mathematics > Numerical Analysis

arXiv:1812.09015 (math)
[Submitted on 21 Dec 2018 (v1), last revised 5 Mar 2019 (this version, v2)]

Title:Navier-Stokes equations on Riemannian manifolds

Authors:Maryam Samavaki, Jukka Tuomela
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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.
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:1812.09015 [math.NA]
  (or arXiv:1812.09015v2 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.1812.09015

Submission history

From: Maryam Samavaki [view email]
[v1] Fri, 21 Dec 2018 09:38:50 UTC (17 KB)
[v2] Tue, 5 Mar 2019 10:22:40 UTC (21 KB)
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