P. G. De-gennes and J. Prost, The physics of liquid crystals, 1993.

G. A. Chechkin, T. S. Ratiu, M. S. Romanov, and V. N. Samokhin, Nematic liquid crystals. Existence and uniqueness of periodic solutions to Ericksen?Leslie equations. Bull, pp.139-151, 2012.

T. S. Ratiu, M. S. Romanov, and G. A. Chechkin, Homogenization of the equations of the dynamics of nematic liquid crystals with inhomogeneous density, J. Math. Sci, vol.186, issue.66, pp.322-329, 2012.

G. A. Chechkin, T. P. Chechkina, T. S. Ratiu, and M. S. Romanov, Nematodynamics and random homogenization Online first, Appl. Anal, 2015.

J. Ericksen, Conservation Laws for Liquid Crystals, Transactions of the Society of Rheology, vol.5, issue.1, pp.22-34, 1961.
DOI : 10.1122/1.548883

J. Ericksen, Hydrostatic theory of liquid crystals, Archive for Rational Mechanics and Analysis, vol.9, issue.1, pp.371-378, 1962.
DOI : 10.1007/BF00253358

F. Leslie, SOME CONSTITUTIVE EQUATIONS FOR ANISOTROPIC FLUIDS, The Quarterly Journal of Mechanics and Applied Mathematics, vol.19, issue.3, pp.357-370, 1966.
DOI : 10.1093/qjmam/19.3.357

F. Leslie, Some constitutive equations for liquid crystals, Arch. Ration. Mech. Anal, vol.28, pp.265-283, 1968.

J. Ericksen, Continuum Theory of Liquid Crystals of Nematic Type, Molecular Crystals, vol.15, issue.1, pp.381-392, 1987.
DOI : 10.1007/BF01511142

F. Leslie, Continuum theory for nematic liquid crystals, Continuum Mechanics and Thermodynamics, vol.148, issue.3, pp.167-175, 1992.
DOI : 10.1007/BF01130288

F. Lin and C. Liu, Existence of Solutions for the Ericksen-Leslie System, Archive for Rational Mechanics and Analysis, vol.154, issue.2, pp.135-15610, 2000.
DOI : 10.1007/s002050000102

F. Gay-balmaz and T. S. Ratiu, The geometric structure of complex fluids, Advances in Applied Mathematics, vol.42, issue.2, pp.176-275, 2009.
DOI : 10.1016/j.aam.2008.06.002

F. H. Lin, Nonlinear theory of defects in nematic liquid crystals; Phase transition and flow phenomena, Communications on Pure and Applied Mathematics, vol.29, issue.6, pp.789-814, 1989.
DOI : 10.1002/cpa.3160420605

F. H. Lin and C. Liu, Nonparabolic dissipative system modeling the ow of liquid crystals, Commun. Pure Appl. Math. XLVIII, pp.501-537, 1995.

S. Shkoller, WELL-POSEDNESS AND GLOBAL ATTRACTORS FOR LIQUID CRYSTALS ON RIEMANNIAN MANIFOLDS, Communications in Partial Differential Equations, vol.117, issue.5-6, pp.1103-1137, 2002.
DOI : 10.2307/2006981

M. C. Hong, Global existence of solutions of the simplified Ericksen???Leslie system in dimension two, Calculus of Variations and Partial Differential Equations, vol.160, issue.1-2, pp.15-36, 2011.
DOI : 10.1007/s00526-010-0331-5

F. H. Lin, J. Y. Liu, and C. Y. Wang, Liquid Crystal Flows in Two Dimensions, Archive for Rational Mechanics and Analysis, vol.60, issue.5, pp.297-336, 2010.
DOI : 10.1007/s00205-009-0278-x

M. C. Hong and Z. P. Xin, Global existence of solutions of the liquid crystal flow for the Oseen???Frank model in <mml:math altimg="si1.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math>, Advances in Mathematics, vol.231, issue.3-4, pp.1364-1400, 2012.
DOI : 10.1016/j.aim.2012.06.009

C. Y. Wang, Well-posedness for the heat flow of harmonic maps and the liquid crystal flow with rough initial data, Archive for Rational Mechanics and Analysis, vol.188, issue.2, pp.1-19, 2011.
DOI : 10.1007/s00205-010-0343-5

F. Jiang, S. Jiang, and D. Wang, Global Weak Solutions to the Equations of Compressible Flow of Nematic Liquid Crystals in Two Dimensions, Archive for Rational Mechanics and Analysis, vol.204, issue.3, pp.403-451, 2014.
DOI : 10.1007/s00205-014-0768-3

M. Hieber, M. Nesensohn, J. Prüss, and K. Schade, Dynamics of nematic liquid crystal flows: The quasilinear approach, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.33, issue.2, 2014.
DOI : 10.1016/j.anihpc.2014.11.001

T. S. Ratiu, M. S. Romanov, V. N. Samokhin, and G. A. Chechkin, Existence and uniqueness theorems in two-dimensional nematodynamics. Finite speed of propagation, Doklady Mathematics, vol.91, issue.3, pp.519-523, 2015.
DOI : 10.1134/S106456241503028X

URL : https://hal.archives-ouvertes.fr/hal-01398390

O. Ladyzhenskaya and N. Uraltseva, Linear and quasilinear elliptic equations, 1968.

S. L. Sobolev, Some applications of functional analysis in mathematical physics, 1991.

V. P. Mikhailov, Partial differential equations, 1978.

T. S. Ratiu, Switzerland e-mail: tudor.ratiu@epfl.ch Vyacheslav N. Samokhin Moscow State University of Printing Art 2A Pryanishnikova ul, Shanghai China Tudor S. Ratiu Section de Mathématiques Mathématiques´MathématiquesÉcole Polytechnique Fédérale de Lausanne 1015 Lausanne, 2016.