Small data global regularity for 3-D Ericksen-Leslie's hyperbolic liquid crystal model without kinematic transport

Abstract

In this article, we consider the Ericksen-Leslie's hyperbolic system for incompressible liquid crystal model without kinematic transport in three spatial dimensions, which is a nonlinear coupling of incompressible Navier-Stokes equations with wave map to ${\mathbb{S}}^2$. Global regularity for small and smooth initial data near the equilibrium is proved. The proof relies on the idea of space-time resonance.

39 pages;accepted by SIAM JMA at Oct. 20, 2020; welcome any coment

References in corpus (2)

• On well-posedness of Ericksen-Leslie's hyperbolic incompressible liquid crystal model
• Global Well-posedness for the Three Dimensional Simplified Inertial Ericksen-Leslie Systems Near Equilibrium

Cited by in corpus (4)

• The zero inertia limit of Ericksen-Leslie's model for liquid crystals
• Small data global regularity for simplified 3-D Ericksen-Leslie's compressible hyperbolic liquid crystal model
• Entropy inequality and energy dissipation of inertial Qian-Sheng model for nematic liquid crystals
• Incompressible limit of the Ericksen-Leslie hyperbolic liquid crystal model in compressible flow