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

TL;DR

This paper proves the local existence and uniqueness of strong solutions for a density-dependent liquid crystal system in three dimensions, using biharmonic regularization and exploiting cancellation properties.

Contribution

It introduces a biharmonic regularization approach and leverages intrinsic cancellations to establish well-posedness for the complex coupled system.

Findings

Established local existence of strong solutions

Proved uniqueness of solutions

Utilized biharmonic regularization and cancellation properties

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.