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

Abstract

In this paper, we study the Cauchy problem to the density-dependent liquid crystal system in ${\mathbb{R}}^3$. 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.

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