Modeling and analysis of the ericksen-leslie equations for nematic liquid crystal flows

Matthias Georg Hieber, Jan W. Prüss

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Citation (Scopus)

Abstract

This survey article discusses various aspects of modeling and analysis of the Ericksen-Leslie equations describing nematic liquid crystal flow both in the isothermal and non-isothermal situation. Of special interest is the development of thermodynamically consistent Ericksen-Leslie models in the general situation based on the entropy principle. The full analytical understanding of the dynamics of the underlying system is then based on this principle and gives rise to a rather complete understanding of the dynamics of this system. Furthermore, well-posedness and long-time behavior results in the weak and strong sense are described for the general Ericksen-Leslie system and various simplifications, ranging from the simplified and penalized model, with or without stretching terms, to the case of general Leslie stress both for incompressible and compressible fluids.

Original languageEnglish
Title of host publicationHandbook of Mathematical Analysis in Mechanics of Viscous Fluids
PublisherSpringer International Publishing
Pages1075-1134
Number of pages60
ISBN (Electronic)9783319133447
ISBN (Print)9783319133430
DOIs
Publication statusPublished - 2018 Apr 19
Externally publishedYes

Fingerprint

Nematic liquid crystals
Nematic Liquid Crystal
liquid crystals
compressible fluids
incompressible fluids
Leslie model
simplification
Modeling
Stretching
Entropy
Compressible Fluid
Long-time Behavior
entropy
Well-posedness
Incompressible Fluid
Simplification
Fluids
Term
Model

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)
  • Engineering(all)

Cite this

Hieber, M. G., & Prüss, J. W. (2018). Modeling and analysis of the ericksen-leslie equations for nematic liquid crystal flows. In Handbook of Mathematical Analysis in Mechanics of Viscous Fluids (pp. 1075-1134). Springer International Publishing. https://doi.org/10.1007/978-3-319-13344-7_26

Modeling and analysis of the ericksen-leslie equations for nematic liquid crystal flows. / Hieber, Matthias Georg; Prüss, Jan W.

Handbook of Mathematical Analysis in Mechanics of Viscous Fluids. Springer International Publishing, 2018. p. 1075-1134.

Research output: Chapter in Book/Report/Conference proceedingChapter

Hieber, MG & Prüss, JW 2018, Modeling and analysis of the ericksen-leslie equations for nematic liquid crystal flows. in Handbook of Mathematical Analysis in Mechanics of Viscous Fluids. Springer International Publishing, pp. 1075-1134. https://doi.org/10.1007/978-3-319-13344-7_26
Hieber MG, Prüss JW. Modeling and analysis of the ericksen-leslie equations for nematic liquid crystal flows. In Handbook of Mathematical Analysis in Mechanics of Viscous Fluids. Springer International Publishing. 2018. p. 1075-1134 https://doi.org/10.1007/978-3-319-13344-7_26
Hieber, Matthias Georg ; Prüss, Jan W. / Modeling and analysis of the ericksen-leslie equations for nematic liquid crystal flows. Handbook of Mathematical Analysis in Mechanics of Viscous Fluids. Springer International Publishing, 2018. pp. 1075-1134
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