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On weak solution to the steady compressible flow of nematic liquid crystals. (English) Zbl 1444.76018

Summary: In this paper, we study the three-dimensional-simplified Ericksen-Leslie system for the steady compressible flow of nematic liquid crystals in a bounded domain. It is proved that the existence of a weak solution for the adiabatic exponent \({\gamma} > 1\) provided the initial direction field in the upper hemisphere.

MSC:

76A15 Liquid crystals
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35Q35 PDEs in connection with fluid mechanics
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