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An Elementary Proof of Eigenvalue Preservation for the Co-rotational Beris-Edwards System

  • Andres Contreras
  • Xiang Xu
  • Wujun Zhang
Article
  • 7 Downloads

Abstract

We study the corotational Beris-Edwards system modeling nematic liquid crystals and revisit the eigenvalue preservation property discussed in Wu et al. (Arch Rational Mech Anal, 2018 https://doi.org/10.1007/s00205-018-1297-2). We give an alternative but direct proof to the eigenvalue preservation of the initial data for the Q-tensor. It is noted that our proof is not only valid in the whole-space case, but in the bounded-domain case as well.

Keywords

Corotational Beris-Edwards system Q-tensor Eigenvalue preservation 

Mathematics Subject Classification

35Q35 35Q30 

Notes

Acknowledgements

We thank the anonymous referees for their careful reading and useful suggestions to improve our paper, especially the observation that leads to Corollary 1.1, which can be considered an improved result of Theorem 1.1. The work of A. Contreras was partially supported by a grant from the Simons Foundation # 426318. And the work of Zhang is supported by the start-up fund from Department of Mathematics, Rutgers University. We want to thank our friends Xavier Lamy, Yuning Liu and Arghir Zarnescu for their kind discussions. In particular, Xu would like to express his gratitude to Arghir for his consistent support and academic communications over a series of topics on the mathematical Q-tensor theory during the past six years. Without his idea proposed in Wu et al. (2018), this paper would not come out.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematical SciencesNew Mexico State UniversityLas CrucesUSA
  2. 2.Department of Mathematics and StatisticsOld Dominion UniversityNorfolkUSA
  3. 3.Department of MathematicsRutgers UniversityPiscatawayUSA

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