Global well-posedness to the compressible nematic liquid crystal flows with large oscillations and vacuum in 3D exterior domains

Abstract

This paper aims at extending our previous work (Y. Liu and X. Zhong, arXiv:2204.06227) to the exterior problem. We show the global well-posedness of strong solutions to a simplified Ericksen–Leslie model of compressible nematic liquid crystal flows in a three-dimensional exterior domain when the initial total energy is sufficiently small. In order to obtain necessary a priori estimates on the boundary, some new analytic techniques are used.