Thermodynamical consistent modeling and analysis of nematic liquid crystal flows

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Citations (Scopus)

Abstract

The general Ericksen-Leslie model for the flow of nematic liquid crystals is reconsidered in the non-isothermal case aiming for thermodynamically consistent models. The non-isothermal simplified model is then investigated analytically. A fairly complete dynamic theory is developed by analyzing these systems as quasilinear parabolic evolution equations in an Lp − Lq-setting. First, the existence of a unique, local strong solution is proved. It is then shown that this solution extends to a global strong solution provided the initial data are close to an equilibrium or the solution is eventually bounded in the natural norm of the underlying state space. In these cases the solution converges exponentially to an equilibrium in the natural state manifold.

Original languageEnglish
Title of host publicationMathematical Fluid Dynamics, Present and Future
PublisherSpringer New York LLC
Pages433-459
Number of pages27
Volume183
ISBN (Print)9784431564553
DOIs
Publication statusPublished - 2016
Externally publishedYes
Event8th CREST-SBM nternational Conference on Mathematical Fluid Dynamics, Present and Future, 2014 - Tokyo, Japan
Duration: 2014 Nov 112014 Nov 14

Other

Other8th CREST-SBM nternational Conference on Mathematical Fluid Dynamics, Present and Future, 2014
CountryJapan
CityTokyo
Period14/11/1114/11/14

Fingerprint

Nematic Liquid Crystal
Strong Solution
Leslie model
Dynamics (theory)
Modeling
Parabolic Equation
Evolution Equation
State Space
Converge
Norm
Model

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Hieber, M. G., & Prüss, J. (2016). Thermodynamical consistent modeling and analysis of nematic liquid crystal flows. In Mathematical Fluid Dynamics, Present and Future (Vol. 183, pp. 433-459). Springer New York LLC. https://doi.org/10.1007/978-4-431-56457-7_15

Thermodynamical consistent modeling and analysis of nematic liquid crystal flows. / Hieber, Matthias Georg; Prüss, Jan.

Mathematical Fluid Dynamics, Present and Future. Vol. 183 Springer New York LLC, 2016. p. 433-459.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Hieber, MG & Prüss, J 2016, Thermodynamical consistent modeling and analysis of nematic liquid crystal flows. in Mathematical Fluid Dynamics, Present and Future. vol. 183, Springer New York LLC, pp. 433-459, 8th CREST-SBM nternational Conference on Mathematical Fluid Dynamics, Present and Future, 2014, Tokyo, Japan, 14/11/11. https://doi.org/10.1007/978-4-431-56457-7_15
Hieber MG, Prüss J. Thermodynamical consistent modeling and analysis of nematic liquid crystal flows. In Mathematical Fluid Dynamics, Present and Future. Vol. 183. Springer New York LLC. 2016. p. 433-459 https://doi.org/10.1007/978-4-431-56457-7_15
Hieber, Matthias Georg ; Prüss, Jan. / Thermodynamical consistent modeling and analysis of nematic liquid crystal flows. Mathematical Fluid Dynamics, Present and Future. Vol. 183 Springer New York LLC, 2016. pp. 433-459
@inproceedings{44f264a1c500435cb5c0bd805f09f7d2,
title = "Thermodynamical consistent modeling and analysis of nematic liquid crystal flows",
abstract = "The general Ericksen-Leslie model for the flow of nematic liquid crystals is reconsidered in the non-isothermal case aiming for thermodynamically consistent models. The non-isothermal simplified model is then investigated analytically. A fairly complete dynamic theory is developed by analyzing these systems as quasilinear parabolic evolution equations in an Lp − Lq-setting. First, the existence of a unique, local strong solution is proved. It is then shown that this solution extends to a global strong solution provided the initial data are close to an equilibrium or the solution is eventually bounded in the natural norm of the underlying state space. In these cases the solution converges exponentially to an equilibrium in the natural state manifold.",
author = "Hieber, {Matthias Georg} and Jan Pr{\"u}ss",
year = "2016",
doi = "10.1007/978-4-431-56457-7_15",
language = "English",
isbn = "9784431564553",
volume = "183",
pages = "433--459",
booktitle = "Mathematical Fluid Dynamics, Present and Future",
publisher = "Springer New York LLC",

}

TY - GEN

T1 - Thermodynamical consistent modeling and analysis of nematic liquid crystal flows

AU - Hieber, Matthias Georg

AU - Prüss, Jan

PY - 2016

Y1 - 2016

N2 - The general Ericksen-Leslie model for the flow of nematic liquid crystals is reconsidered in the non-isothermal case aiming for thermodynamically consistent models. The non-isothermal simplified model is then investigated analytically. A fairly complete dynamic theory is developed by analyzing these systems as quasilinear parabolic evolution equations in an Lp − Lq-setting. First, the existence of a unique, local strong solution is proved. It is then shown that this solution extends to a global strong solution provided the initial data are close to an equilibrium or the solution is eventually bounded in the natural norm of the underlying state space. In these cases the solution converges exponentially to an equilibrium in the natural state manifold.

AB - The general Ericksen-Leslie model for the flow of nematic liquid crystals is reconsidered in the non-isothermal case aiming for thermodynamically consistent models. The non-isothermal simplified model is then investigated analytically. A fairly complete dynamic theory is developed by analyzing these systems as quasilinear parabolic evolution equations in an Lp − Lq-setting. First, the existence of a unique, local strong solution is proved. It is then shown that this solution extends to a global strong solution provided the initial data are close to an equilibrium or the solution is eventually bounded in the natural norm of the underlying state space. In these cases the solution converges exponentially to an equilibrium in the natural state manifold.

UR - http://www.scopus.com/inward/record.url?scp=85009802338&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85009802338&partnerID=8YFLogxK

U2 - 10.1007/978-4-431-56457-7_15

DO - 10.1007/978-4-431-56457-7_15

M3 - Conference contribution

SN - 9784431564553

VL - 183

SP - 433

EP - 459

BT - Mathematical Fluid Dynamics, Present and Future

PB - Springer New York LLC

ER -