Regularity of the solutions to the liquid crystal equations with small rough data

In [30], the author has proved the existence of Koch–Tataru [12] type solution to the incompressible nematic liquid crystal flow with initial data (u0,d0)(u0,d0) in BMO−1×BMOBMO−1×BMO. In this paper, we shall present that the solution in [30] has arbitrary spatial regularity. Furthermore, we shall give the decay estimates for any space derivative.