Title: Non-uniqueness of the Leray-Hopf solutions in the hyperbolic setting
Authors: Chan, Chi Hin
Czubak, Magdalena
Department of Applied Mathematics
Keywords: Navier-Stokes;Leray-Hopf;non-uniqueness;hyperbolic space;Liouville theorem
Issue Date: 1-Mar-2013
Abstract: The Leray-Hopf solutions to the Navier-Stokes equation are known to be unique on R-2. We show the uniqueness of the Leray-Hopf solutions breaks down on H-2(-a(2)), the two dimensional hyperbolic space with constant sectional curvature -a(2). We also obtain a corresponding result on a more general negatively curved manifold for a modified geometric version of the Navier-Stokes equation. Finally, as a corollary we also show a lack of the Liouville theorem in the hyperbolic setting both in two and three dimensions.
URI: http://hdl.handle.net/11536/21403
ISSN: 1548-159X
Volume: 10
Issue: 1
Begin Page: 43
End Page: 77
Appears in Collections:Articles