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arXiv · 1910.05175

Vorticity, Helicity, Intrinsinc geometry for Navier-Stokes equations

Shizan Fang·Zhongmin Qian
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Abstract

We will consider the Navier-Stokes equation on a Riemannian manifold M with Ricci tensor bounded below, the involved Laplacian operator is De Rham-Hodge Laplacian. The novelty of this work is to introduce a family of connections which are related to solutions of the Navier-Stokes equation, so that vorticity and helicity can be linked through the associated time-dependent Ricci tensor in intrinsic way in the case where dim(M) = 3. MSC 2010: 35Q30, 58J65

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Shizan Fang, Zhongmin Qian. 2019-10-11. Vorticity, Helicity, Intrinsinc geometry for Navier-Stokes equations. https://arxiv.org/abs/1910.05175

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