SMALL DATA GLOBAL REGULARITY FOR THE 3-D ERICKSEN-LESLIE HYPERBOLIC LIQUID CRYSTAL MODEL WITHOUT KINEMATIC TRANSPORT

摘要

In this article, we consider the hyperbolic Ericksen-Leslie system for incompressible liquid crystals without kinematic transport in three spatial dimensions, which is a nonlinear coupling of incompressible NavierStokes equations with wave map to 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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