Local well-posedness of strong solutions to density-dependent liquid crystal system

In this paper, we study the Cauchy problem to the density-dependent liquid crystal system in R3. We establish the local existence and uniqueness of strong solutions to this system. In order to overcome the difficulties caused by the high order coupling terms, a biharmonic regularization of the system, as an auxiliary system, is introduced, and we make full use of the intrinsic cancellation properties between the high order coupling terms.