Dynamics of the Ericksen–Leslie Equations with General Leslie Stress II: The Compressible Isotropic Case

Abstract

In this article, the non-isothermal compressible Ericksen–Leslie system for nematic liquid crystals subject to general Leslie stress is considered. It is shown that this system is locally well-posed within the $$L_q$$ -setting and that for initial data close to equilibria points (which are identical with the ones for the incompressible situation), the solution exists globally. Moreover, any global solution which does not develop singularities converges to an equilibrium in the topology of the natural state manifold. Note that no structural assumptions on the Leslie coefficients are imposed and, in particular, Parodi’s relation is not being assumed. The results can be viewed as an extension of the studies in Hieber and Pruss (Math Ann 369:977–996, 2017) for the incompressible case to the compressible situation.