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

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