On the Existence of Solutions to the Nematic Liquid Crystal Flow in Weak－Lp Spaces

In recent paper, the global solutions to incompressible nematic liquid crystal flow in high dimensions is considered. The authors establish the global existence of the Cauchy problem of the nematic liquid crystal flow in $R^n$ for any initial data $(u_0,d_0)$ with small $\|u_0\|_{(n,\infty)}+\|\nabla d_0\|_{(n,\infty)}.$ The method is based on a priori estimates and Fixed Point Theorem.