title: Euler and Navier-Stokes equations on the hyperbolic plane.
abstract: We show that nonuniqueness of the Leray-Hopf solutions of the Navier-Stokes equation on the hyperbolic plane (2) observed by Chan and Czubak is a consequence of the Hodge decomposition. We show that this phenomenon does not occur on (n) whenever n ≥ 3. We also describe the corresponding general Hamiltonian framework of hydrodynamics on complete Riemannian manifolds, which includes the hyperbolic setting.
authors.affiliation: School of Mathematics, Institute for Advanced Study, Princeton, NJ 08450, USA. khesin@math.toronto.edu
authors.forename: Boris
authors.initials: B
authors.lastname: Khesin
authors.forename: Gerard
authors.initials: G
authors.lastname: Misiolek