Nematodynamics and random homogenization. Issue 10 (2nd October 2016)

• Record Type: Journal Article
• Authors: Chechkin, Gregory A.; Chechkina, Tatiana P.; Ratiu, Tudor S.; Romanov, Maksim S.
• Is Part Of: Applicable analysis. Volume 95:Issue 10(2016)
• Page Start: 2243
• Page End: 2253
• Publication Date: 2016-10-02
• Subjects: liquid crystals -- Ericksen–Leslie equations -- nematodynamics -- random homogenization -- director field -- speed of propagation; 76A15 -- 35K61 -- 35A01 -- 35A02; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2015.1036241
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : 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.