About: On the long-time behavior of some mathematical models for nematic liquid crystals

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	A model describing the evolution of a liquid crystal substance in the nematic phase is investigated in terms of two basic state variables: the velocity field u and the director field d, representing the preferred orientation of molecules in a neighborhood of any point in a reference domain. After recalling a known existence result, we investigate the longtime behavior of weak solutions. In particular, we show that any solution trajectory admits a non-empty ω-limit set containing only stationary solutions. Moreover, we give a number of sufficient conditions in order that the ω-limit set contains a single point. Our approach improves and generalizes existing results on the same problem. A model describing the evolution of a liquid crystal substance in the nematic phase is investigated in terms of two basic state variables: the velocity field u and the director field d, representing the preferred orientation of molecules in a neighborhood of any point in a reference domain. After recalling a known existence result, we investigate the longtime behavior of weak solutions. In particular, we show that any solution trajectory admits a non-empty ω-limit set containing only stationary solutions. Moreover, we give a number of sufficient conditions in order that the ω-limit set contains a single point. Our approach improves and generalizes existing results on the same problem. (en)
Title	On the long-time behavior of some mathematical models for nematic liquid crystals On the long-time behavior of some mathematical models for nematic liquid crystals (en)
skos:prefLabel	On the long-time behavior of some mathematical models for nematic liquid crystals On the long-time behavior of some mathematical models for nematic liquid crystals (en)
skos:notation	RIV/67985840:_____/13:00374133!RIV13-AV0-67985840
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(LC06052), Z(AV0Z10190503)
http://linked.open...iv/cisloPeriodika	3-4
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Petzeltová, Hana
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Matematický ústav AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	93898
http://linked.open...ai/riv/idVysledku	RIV/67985840:_____/13:00374133
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	nematic liquid crystals; long-time behavior; flows (en)
http://linked.open.../riv/klicoveSlovo	flows long-time behavior nematic liquid crystals
http://linked.open...odStatuVydavatele	DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV	[7260AA2ECD13]
http://linked.open...i/riv/nazevZdroje	Calculus of Variations and Partial Differential Equations
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	The Nečas Center for Mathematical Modeling
http://linked.open...UplatneniVysledku	2013
http://linked.open...v/svazekPeriodika	46
http://linked.open...iv/tvurceVysledku	Petzeltová, Hana Rocca, E. Schimperna, G.
http://linked.open...ain/vavai/riv/wos	000314709300008
http://linked.open...n/vavai/riv/zamer	Rozvoj a prohloubení obecných matematických poznatků a jejich užití v dalších vědních oborech a v praxi
issn	0944-2669
number of pages	17 (xsd:int)
http://bibframe.org/vocab/doi	10.1007/s00526-012-0496-1

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