Communications in Mathematical Sciences

Volume 13 (2015)

Number 7

Nonlinear continuum theory of smectic-C liquid crystals

Pages: 1787 – 1801

DOI: http://dx.doi.org/10.4310/CMS.2015.v13.n7.a7

Authors

Qiao Tang (School of Mathematical Sciences, Beijing Normal University, Beijing, China)

Hui Zhang (Laboratory of Mathematics and Complex Systems, Ministry of Education, School of Mathematical Sciences, Beijing Normal University, Beijing, China)

Abstract

Here we develop a model of smectic-C liquid crystals by forming their hydrostatic and hydrodynamic theories which are motivated by W.N. E’s work [Arch. Rational Mech. Anal., 137 (1997)]. A simplified model is also presented. In order to prove the rationality of the model, we establish the energy dissipative relation of the new model. Meanwhile, we verify that the system can also be obtained using asymptotic analysis when both the fluid and layers are incompressible.

Keywords

continuum theory, smectic liquid crystals, smectic-C, hydrodynamic equations, kinetic theory

2010 Mathematics Subject Classification

35Q35, 35Q51, 76D07, 80A17

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