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In this paper, we investigate the steady simplified Ericksen-Leslie system.For three dimension, we obtain Liouville theorems if $u$ and $\nabla d$ satisfythe Galdi's[1] condition, or some decay conditions. Note that the simplifiedEricksen-Leslie system becomes Navier-Stokes equations when $d$ is constantvector.

Liouville theorem for steady-state solutions of simplified Ericksen-Leslie system