Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (1): 126-141.

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A Formal Analysis on the Large Ericksen Number Limit for the Incompressible Hyperbolic Ericksen-Leslie System of Liquid Crystals

Feng Cheng()   

  1. Hubei Key Laboratory of Applied Mathematics & Faculty of Mathematics and Statistics, Hubei University, Wuhan 430062
  • Received:2020-03-15 Online:2021-02-26 Published:2021-01-29

Abstract:

In this paper, we consider the parameterized incompressible hyperbolic Ericksen-Leslie system of liquid crystals. Formally, letting the parameter vanish, we prove that the limit system admits a local classical solution. Moreover, we formally obtained an estimate on the difference between the parameterized Ericksen-Leslie's incompressible hyperbolic liquid crystal model and the corresponding limit system, which corresponds to a formal energy estimate of the difference of the classical solutions in $L^2$ space.

Key words: Liquid crystals, Ericksen-Leslie system, Classical solution, Large Ericksen number limit

CLC Number: 

  • O175.25
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