An Elementary Proof of Eigenvalue Preservation for the Co-rotational Beris-Edwards System
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.
KeywordsCorotational Beris-Edwards system Q-tensor Eigenvalue preservation
Mathematics Subject Classification35Q35 35Q30
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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