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Nonparabolic dissipative systems modeling the flow of liquid crystals. (English) Zbl 0842.35084
Summary: We study a simplified system which retains most of the interesting mathematical properties of the original Ericksen-Leslie equations for the flow of liquid crystals. This is a coupled nonparabolic dissipative dynamic system. We derive several energy laws which enable us to prove the global existence of the weak solutions and the classical solutions. We also discuss uniqueness and some stability properties of the system.

MSC:
35Q35 PDEs in connection with fluid mechanics
76A15 Liquid crystals
35D05 Existence of generalized solutions of PDE (MSC2000)
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35B35 Stability in context of PDEs
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