The Euler and Navier-Stokes equations on the hyperbolic plane
Analysis of PDEs
2015-06-05 v1 Mathematical Physics
Differential Geometry
math.MP
Abstract
We show that non-uniqueness of the Leray-Hopf solutions of the Navier--Stokes equation on the hyperbolic plane observed in arXiv:1006.2819 is a consequence of the Hodge decomposition. We show that this phenomenon does not occur on the hyperbolic spaces of higher dimension. We also describe the corresponding general Hamiltonian setting of hydrodynamics on complete Riemannian manifolds, which includes the hyperbolic setting.
Cite
@article{arxiv.1205.5322,
title = {The Euler and Navier-Stokes equations on the hyperbolic plane},
author = {Boris Khesin and Gerard Misiolek},
journal= {arXiv preprint arXiv:1205.5322},
year = {2015}
}
Comments
6 pages