  We consider the simplified Ericksen-Leslie model in three dimensional bounded
Lipschitz domains. Applying a semilinear approach, we prove local and global
well-posedness (assuming a smallness condition on the initial data) in critical
spaces for initial data in $L^3_{\sigma}$ for the fluid and $W^{1,3}$ for the
director field. The analysis of such models, so far, has been restricted to
domains with smooth boundaries.
