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Statements

Subject Item
n2:RIV%2F67985840%3A_____%2F11%3A00391072%21RIV13-MSM-67985840
rdf:type
n4:Vysledek skos:Concept
dcterms: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.
dcterms:title
On a non-isothermal model for nematic liquid crystals On a non-isothermal model for nematic liquid crystals
skos:prefLabel
On a non-isothermal model for nematic liquid crystals On a non-isothermal model for nematic liquid crystals
skos:notation
RIV/67985840:_____/11:00391072!RIV13-MSM-67985840
n4:predkladatel
n12:ico%3A67985840
n3:aktivita
n15:Z n15:P
n3:aktivity
P(GA201/09/0917), P(LC06052), Z(AV0Z10190503)
n3:cisloPeriodika
1
n3:dodaniDat
n19:2013
n3:domaciTvurceVysledku
n6:4334256
n3:druhVysledku
n20:J
n3:duvernostUdaju
n7:S
n3:entitaPredkladatele
n9:predkladatel
n3:idSjednocenehoVysledku
217955
n3:idVysledku
RIV/67985840:_____/11:00391072
n3:jazykVysledku
n18:eng
n3:klicovaSlova
Navier-Stokes equations; system; flows
n3:klicoveSlovo
n11:flows n11:Navier-Stokes%20equations n11:system
n3:kodStatuVydavatele
GB - Spojené království Velké Británie a Severního Irska
n3:kontrolniKodProRIV
[0019580818A3]
n3:nazevZdroje
Nonlinearity
n3:obor
n14:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
3
n3:projekt
n16:LC06052 n16:GA201%2F09%2F0917
n3:rokUplatneniVysledku
n19:2011
n3:svazekPeriodika
24
n3:tvurceVysledku
Feireisl, Eduard Rocca, E. Schimperna, G.
n3:wos
000285343600013
n3:zamer
n8:AV0Z10190503
s:issn
0951-7715
s:numberOfPages
15
n17:doi
10.1088/0951-7715/24/1/012