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Dynamics and Flow Effects in the Beris-Edwards System Modeling Nematic Liquid Crystals

  • Hao Wu
  • Xiang Xu
  • Arghir Zarnescu
Article

Abstract

We consider the Beris-Edwards system modelling incompressible liquid crystal flows of nematic type. This couples a Navier-Stokes system for the fluid velocity with a parabolic reaction-convection-diffusion system for the Q-tensors describing the average orientation of liquid crystal molecules. In this paper, we study the effect that the flow has on the dynamics of the Q-tensors by considering two fundamental aspects: the preservation of the eigenvalue-range and the dynamical emergence of defects in the limit of large Ericksen number.

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Notes

Acknowledgements

H. Wu is partially supported by NNSFC grant No. 11631011. X. Xu is supported by the start-up fund from the Department of Mathematics and Statistics at Old Dominion University. A. Zarnescu is partially supported by a Grant of the Romanian National Authority for Scientific Research and Innovation, CNCS-UEFISCDI, project number PN-II-RU-TE-2014-4-0657; by the Basque Government through the BERC 2018-2021 program; and by SpanishMinistry of Economy and CompetitivenessMINECO through BCAM Severo Ochoa excellence accreditation SEV-2013-0323 and through project MTM2017-82184-R funded by (AEI/FEDER, UE) and acronym “DESFLU”; and by Leverhulme grant RPG 2014-226. All authors would like to thank the anonymous referee for the careful reading of an initial version of this manuscript and for the very helpful comments that allowed us to improve the paper.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematical Sciences and Shanghai, Key Laboratory for Contemporary Applied MathematicsFudan UniversityShanghaiChina
  2. 2.Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University)Ministry of EducationShanghaiChina
  3. 3.Department of Mathematics and StatisticsOld Dominion UniversityNorfolkUSA
  4. 4.IKERBASQUE, Basque Foundation for ScienceBilbaoSpain
  5. 5.BCAM, Basque Center for Applied MathematicsBilbaoSpain
  6. 6.“Simion Stoilow” Institute of the Romanian AcademyBucharestRomania

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