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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 three basic state variables: the absolute temperature theta, the velocity field u and the director field d, representing preferred orientation of molecules in a neighbourhood of any point of a reference domain. The time evolution of the velocity field is governed by the incompressible Navier-Stokes system, with a non-isotropic stress tensor depending on the gradients of the velocity and of the director field d, where the transport (viscosity) coefficients vary with temperature. The dynamics of d is described by means of a parabolic equation of Ginzburg-Landau type, with a suitable penalization term to relax the constraint vertical bar d vertical bar = 1. The system is supplemented by a heat equation, where the heat flux is given by a variant of Fourier's law, depending also on the director field d. The proposed model is shown to be compatible with first and second laws of thermodynamics, and the existence of global-in-time weak solutions for the resulting PDE system is established, without any essential restriction on the size of the data. A model describing the evolution of a liquid crystal substance in the nematic phase is investigated in terms of three basic state variables: the absolute temperature theta, the velocity field u and the director field d, representing preferred orientation of molecules in a neighbourhood of any point of a reference domain. The time evolution of the velocity field is governed by the incompressible Navier-Stokes system, with a non-isotropic stress tensor depending on the gradients of the velocity and of the director field d, where the transport (viscosity) coefficients vary with temperature. The dynamics of d is described by means of a parabolic equation of Ginzburg-Landau type, with a suitable penalization term to relax the constraint vertical bar d vertical bar = 1. The system is supplemented by a heat equation, where the heat flux is given by a variant of Fourier's law, depending also on the director field d. The proposed model is shown to be compatible with first and second laws of thermodynamics, and the existence of global-in-time weak solutions for the resulting PDE system is established, without any essential restriction on the size of the data. (en)
Title	On a non-isothermal model for nematic liquid crystals On a non-isothermal model for nematic liquid crystals (en)
skos:prefLabel	On a non-isothermal model for nematic liquid crystals On a non-isothermal model for nematic liquid crystals (en)
skos:notation	RIV/67985840:_____/11:00391072!RIV13-MSM-67985840
http://linked.open...avai/predkladatel	Matematický ústav AV ČR, v. v. i.
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA201/09/0917), P(LC06052), Z(AV0Z10190503)
http://linked.open...iv/cisloPeriodika	1
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Feireisl, Eduard
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	217955
http://linked.open...ai/riv/idVysledku	RIV/67985840:_____/11:00391072
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Navier-Stokes equations; system; flows (en)
http://linked.open.../riv/klicoveSlovo	Navier-Stokes equations flows system
http://linked.open...odStatuVydavatele	GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV	[0019580818A3]
http://linked.open...i/riv/nazevZdroje	Nonlinearity
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	Mathematical and computer analysis of the evolution processes in nonlinear viscoelastic fluid-like materials The Nečas Center for Mathematical Modeling
http://linked.open...UplatneniVysledku	2011
http://linked.open...v/svazekPeriodika	24
http://linked.open...iv/tvurceVysledku	Feireisl, Eduard Rocca, E. Schimperna, G.
http://linked.open...ain/vavai/riv/wos	000285343600013
http://linked.open...n/vavai/riv/zamer	Rozvoj a prohloubení obecných matematických poznatků a jejich užití v dalších vědních oborech a v praxi
issn	0951-7715
number of pages	15 (xsd:int)
http://bibframe.org/vocab/doi	10.1088/0951-7715/24/1/012
is http://linked.open...avai/riv/vysledek of	On a non-isothermal model for nematic liquid crystals

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