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Nematic liquid crystals in Lipschitz domains. (English) Zbl 1393.76009

Summary: We consider the simplified Ericksen-Leslie model in three-dimensional bounded Lipschitz domains. Applying a semilinear approach, we prove local and global well-posedness (assuming a smallness condition on the initial data) in critical spaces for initial data in \(L^3_{\sigma}\) for the fluid and \(W^{1,3}\) for the director field. The analysis of such models, so far, has been restricted to domains with smooth boundaries.

MSC:

76A15 Liquid crystals
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
35Q35 PDEs in connection with fluid mechanics
47D06 One-parameter semigroups and linear evolution equations
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