Well-posedness for the heat flow of harmonic maps and the liquid crystal flow with rough initial data

Abstract

We investigate the well-posedness of (1) the heat flow of harmonic maps from \({\mathbb R^n}\) to a compact Riemannian manifold N without boundary for initial data in BMO; and (2) the hydrodynamic flow (u, d) of nematic liquid crystals on \({\mathbb R^n}\) for initial data in BMO−1 × BMO.