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
Description
Vorticity, Helicity, Intrinsinc geometry for Navier-Stokes equations
%0 Generic
%1 fang2019vorticity
%A Fang, Shizan
%A Qian, Zhongmin
%D 2019
%K 35q30-navier-stokes-equations
%T Vorticity, Helicity, Intrinsinc geometry for Navier-Stokes equations
%U http://arxiv.org/abs/1910.05175
%X 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
@misc{fang2019vorticity,
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},
added-at = {2020-07-20T21:59:11.000+0200},
author = {Fang, Shizan and Qian, Zhongmin},
biburl = {https://www.bibsonomy.org/bibtex/2f8f7e26b8b2059ee86574439b7611993/gdmcbain},
description = {Vorticity, Helicity, Intrinsinc geometry for Navier-Stokes equations},
interhash = {542280f91a9d14e734a8d3c545857e0e},
intrahash = {f8f7e26b8b2059ee86574439b7611993},
keywords = {35q30-navier-stokes-equations},
note = {cite arxiv:1910.05175},
timestamp = {2020-07-20T21:59:11.000+0200},
title = {Vorticity, Helicity, Intrinsinc geometry for Navier-Stokes equations},
url = {http://arxiv.org/abs/1910.05175},
year = 2019
}