Solutions of incompressible hydrodynamic flow of liquid crystals

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Local existence and uniqueness of strong solutions to the Navier-Stokes equations with nonnegative density (2016, background): “Specifically, one can weaken the regularity assumptions and drop the compatibility conditions on the initial data stated in [6, 8, 13, 14, 16, 21, 32, 33], without destroying the existence and uniqueness”
Regularity and Existence of Global Solutions to the Ericksen–Leslie System in $${\mathbb{R}^2}$$R2 (2013, background): “10) has been proved by Ding-Wen [4], the blow-up criterion of local strong solutions of (1.”