Communications in Mathematical Sciences

Volume 12 (2014)

Number 2

Evolution of non-isothermal Landau–de Gennes nematic liquid crystals flows with singular potential

Pages: 317 – 343

DOI: http://dx.doi.org/10.4310/CMS.2014.v12.n2.a6

Authors

Eduard Feireisl (Institute of Mathematics of the Czech Academy of Sciences, Praha, Czech Republic)

Elisabetta Rocca (Dipartimento di Matematica “F. Enriques”, Università di Milano, Italy)

Giulio Schimperna (Dipartimento di Matematica, Università di Pavia, Italy)

Arghir Zarnescu (Pevensey III, University of Sussex, Falmer, United Kingdom)

Abstract

We discuss a 3D model describing the time evolution of nematic liquid crystals in the framework of Landau-de Gennes theory, where the natural physical constraints are enforced by a singular free energy bulk potential proposed by J.M. Ball and A. Majumdar. The thermal effects are present through the component of the free energy that accounts for intermolecular interactions. The model is consistent with the general principles of thermodynamics and mathematically tractable. We identify the a priori estimates for the associated system of evolutionary partial differential equations and construct global-in-time weak solutions for arbitrary physically relevant initial data.

Keywords

liquid crystals, global existence of weak solutions, Navier-Stokes equations

2010 Mathematics Subject Classification

35D30, 35Q30, 74G25, 76A15

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