ON DISSIPATIVE SOLUTIONS TO A SIMPLIFIED HYPERBOLIC ERICKSEN-LESLIE SYSTEM OF LIQUID CRYSTALS

摘要

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.

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