Non-isothermal General Ericksen-Leslie System: Derivation, Analysis and Thermodynamic Consistency

We derive a model describing the evolution of a nematic liquid-crystal material under the action of thermal effects. The first and second laws of thermodynamics lead to an extension of the general Ericksen-Leslie system where the Leslie stress tensor and the Oseen-Frank energy density are considered in their general forms. The work postulate proposed by Ericksen-Leslie is traduced in terms of entropy production.We finally analyze the global-in-time well-posedness of the system for small initial data in the framework of Besov spaces.