ICTS

In this talk, we shall discuss the simplified Ericksen–Leslie model for nematic liquid crystals in three dimensional bounded Lipschitz domains. Applying a semilinear approach, we shall discuss the proof of local and global well-posedness (assuming a smallness condition on the initial data) in critical spaces for initial data in L 3 σ for the fluid and W1,3 for the director field. The analysis of such models, so far, has been restricted to domains with smooth boundaries.