Nematodynamics and random homogenization

We study the homogenization problem for the system of equations of dynamics of a mixture of liquid crystals with random structure. We consider a simplified form of the Ericksen-Leslie equations for an incompressible medium with inhomogeneous density with random structure. Under the assumption that r...

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Bibliographic Details
Published in:Applicable analysis 2016-10, Vol.95 (10), p.2243-2253
Main Authors: Chechkin, Gregory A., Chechkina, Tatiana P., Ratiu, Tudor S., Romanov, Maksim S.
Format: Article
Language:English
Subjects:
Convergence
Crystals
director field
Dynamic structural analysis
Dynamical systems
Dynamics
Ericksen-Leslie equations
Homogenization
Homogenizing
Liquid crystals
Mathematical analysis
Mathematics
nematodynamics
Propagation
random homogenization
speed of propagation
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Summary:We study the homogenization problem for the system of equations of dynamics of a mixture of liquid crystals with random structure. We consider a simplified form of the Ericksen-Leslie equations for an incompressible medium with inhomogeneous density with random structure. Under the assumption that randomness is statistically homogeneous and ergodic, we construct the limit problem and prove almost sure convergence of solutions of the original problem to the solution of the limit (homogenized) problem.
ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2015.1036241