Global existence and regularity of solutions for active liquid crystals

Chen, Gui-Qiang and Majumdar, Apala and Wang, Dehua and Zhang, Rongfang (2017) Global existence and regularity of solutions for active liquid crystals. Journal of Differential Equations, 263 (1). pp. 202-239. ISSN 0022-0396

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    Abstract

    We study the hydrodynamics of active liquid crystals in the Beris-Edwards hydrodynamic framework with the Landau-de Gennes Q-tensor order parameter to describe liquid crystalline ordering. The existence of global weak solutions in two and three spatial dimensions is established. In the two-dimensional case, by the Littlewood-Paley decomposition, the higher regularity of the weak solutions and the weak-strong uniqueness are also obtained.