Thermodynamical consistent modeling and analysis of nematic liquid crystal flows

Matthias Georg Hieber, Jan Prüss

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

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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