Vorticity, Helicity, Intrinsinc geometry for Navier-Stokes equations

2019/10/11 by Shizan Fang, Zhongmin Qian, Fang, Shizan +1
Engineering · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Cosmology and Gravitation Theories #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #Probability (math.PR) #math.AP #math.PR

paper · pdf · doi:10.48550/arxiv.1910.05175

arxiv created 2019/10/11 · openalex publication_date 2019/10/11 · arxiv updated 2019/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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

Citations

• The incompressible Navier-Stokes equations on non-compact manifolds

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