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arXiv · 1812.08341

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

Jiaxi Huang·Ning Jiang·Yi-Long Luo·Lifeng Zhao
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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.

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Jiaxi Huang, Ning Jiang, Yi-Long Luo, Lifeng Zhao. 2018-12-20. Small data global regularity for 3-D Ericksen-Leslie's hyperbolic liquid crystal model without kinematic transport. https://doi.org/10.1137/20m1322625

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