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

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arxiv 1812.08341 v2 pith:E57SZSGF submitted 2018-12-20 math.AP

Jiaxi Huang , Ning Jiang , Yi-Long Luo , Lifeng Zhao This is my paper · ORCID
classification math.AP
keywords crystaldataericksen-leslieglobalhyperbolicincompressiblekinematicliquid
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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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