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On dissipative solutions to a simplified hyperbolic Ericksen-Leslie system of liquid crystals. (English) Zbl 1496.35309

Summary: We study dissipative solutions to a 3D simplified hyperbolic Ericksen-Leslie system for liquid crystals with Ginzburg-Landau approximation. First, we establish a weak-strong stability principle, which leads to a suitable notion of dissipative solutions to the hyperbolic Ericksen-Leslie system. Then, we introduce a regularized system to approximate the original system, for which we can prove the existence of global-in-time weak solutions. Finally, we prove that there is at least one dissipative solution for this simplified hyperbolic Ericksen-Leslie system.

MSC:

35Q35 PDEs in connection with fluid mechanics
35Q56 Ginzburg-Landau equations
76A15 Liquid crystals
35L51 Second-order hyperbolic systems
35D30 Weak solutions to PDEs
35B65 Smoothness and regularity of solutions to PDEs
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
82D30 Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)
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