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Liquid crystal flow: Dynamic and static configurations. (English) Zbl 0956.35104

Summary: We consider a system modeling the flow of nematic liquid crystals with variable degrees of orientation. Although the set of constitutive equations involves many different parameters, the flow behavior is determined mostly by three nondimensional parameters, i.e., the Ericksen number, the Reynolds number, and the interface number. We establish a dissipative relation of the system in general domains. In the case of plane Poiseuille flow, we prove existence and regularity of solutions. Moreover, we discuss the stationary configurations with a large number of defects due to the large Ericksen number of the flow.

MSC:

35Q35 PDEs in connection with fluid mechanics
35D05 Existence of generalized solutions of PDE (MSC2000)
76A05 Non-Newtonian fluids
35D10 Regularity of generalized solutions of PDE (MSC2000)
76A15 Liquid crystals
76D05 Navier-Stokes equations for incompressible viscous fluids
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
76D27 Other free boundary flows; Hele-Shaw flows
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