Dynamics of the Ericksen-Leslie Model for Nematic Liquid Crystal Flow with General Leslie Stress

Dynamics of the Ericksen-Leslie Model for Nematic Liquid Crystal Flow with General Leslie Stress

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Matthias Hieber , TU Darmstadt
Fine Hall 110

Consider the Ericksen-Leslie model for the flow of nematic liquid crystals in a bounded domain with general Leslie stress in the iso- and nonisothermal setting. We discuss recent local and global well-posedness results in the strong sense for this system and describe in addition the dynamical behaviour of its solutions. Our approach is based on the entropy principle and maximal $L^p$-estimates for the linearized system. It is remarkable that for these results no structural conditions on the Leslie coefficients are imposed and that in particular Parodi's relation is not being assumed. This is joint work with Jan Pruess.