Thermodynamical consistent modeling and analysis of nematic liquid crystal flows

Matthias Georg Hieber; Jan Prüss

doi:10.1007/978-4-431-56457-7_15

Thermodynamical consistent modeling and analysis of nematic liquid crystal flows

Matthias Georg Hieber, Jan Prüss^*

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

12 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 L_p − L_q-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 language	English
Title of host publication	Mathematical Fluid Dynamics, Present and Future
Publisher	Springer New York LLC
Pages	433-459
Number of pages	27
Volume	183
ISBN (Print)	9784431564553
DOIs	https://doi.org/10.1007/978-4-431-56457-7_15
Publication status	Published - 2016
Externally published	Yes
Event	8th CREST-SBM nternational Conference on Mathematical Fluid Dynamics, Present and Future, 2014 - Tokyo, Japan Duration: 2014 Nov 11 → 2014 Nov 14

Other

Other	8th CREST-SBM nternational Conference on Mathematical Fluid Dynamics, Present and Future, 2014
Country/Territory	Japan
City	Tokyo
Period	14/11/11 → 14/11/14

ASJC Scopus subject areas

Mathematics(all)

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

Cite this

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

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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.",

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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.

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Thermodynamical consistent modeling and analysis of nematic liquid crystal flows

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