Non-uniqueness of the Leray-Hopf solutions in the hyperbolic setting

dc.citation.epage	77	en_US
dc.citation.issue	1	en_US
dc.citation.spage	43	en_US
dc.citation.volume	10	en_US
dc.citation.woscount	1
dc.contributor.author	Chan, Chi Hin	en_US
dc.contributor.author	Czubak, Magdalena	en_US
dc.contributor.department	應用數學系	zh_TW
dc.contributor.department	Department of Applied Mathematics	en_US
dc.date.accessioned	2014-12-08T15:29:51Z
dc.date.available	2014-12-08T15:29:51Z
dc.date.issued	2013-03-01	en_US
dc.description.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.	en_US
dc.identifier.issn	1548-159X	en_US
dc.identifier.journal	DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS	en_US
dc.identifier.uri	https://ir.lib.nycu.edu.tw/handle/11536/21403
dc.identifier.wosnumber	WOS:000316446100003
dc.language.iso	en_US	en_US
dc.subject	Navier-Stokes	en_US
dc.subject	Leray-Hopf	en_US
dc.subject	non-uniqueness	en_US
dc.subject	hyperbolic space	en_US
dc.subject	Liouville theorem	en_US
dc.title	Non-uniqueness of the Leray-Hopf solutions in the hyperbolic setting	en_US
dc.type	Article	en_US

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