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.

中文翻译：

---

关于简化的双曲Ericksen-Leslie液晶系统的耗散解

我们用Ginzburg-Landau近似研究液晶的3D简化双曲Ericksen-Leslie系统的耗散解。首先，我们建立了弱强稳定性原理，这导致了对双曲线Ericksen-Leslie系统的耗散解的合适概念。然后，我们引入一个正则化的系统来逼近原始系统，为此我们可以证明存在全局及时弱解。最后，我们证明了这种简化的双曲Ericksen-Leslie系统至少有一种耗散解决方案。