%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 }