Cheng, Feng; Jiang, Ning; Luo, Yi-Long On dissipative solutions to a simplified hyperbolic Ericksen-Leslie system of liquid crystals. (English) Zbl 1496.35309 Commun. Math. Sci. 19, No. 1, 175-192 (2021). 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. Cited in 2 Documents 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) Keywords:Ericksen-Leslie system; dissipative solution; weak strong uniqueness PDFBibTeX XMLCite \textit{F. Cheng} et al., Commun. Math. Sci. 19, No. 1, 175--192 (2021; Zbl 1496.35309) Full Text: DOI