Global small solutions of the compressible nematic liquid crystal flow in a bounded domain
Volume 124 / 2020
Annales Polonici Mathematici 124 (2020), 47-59
MSC: 35Q30, 35Q35, 76D03.
DOI: 10.4064/ap181215-18-5
Published online: 31 October 2019
Abstract
We study the 3D compressible nematic liquid crystal flow in a bounded domain. We first prove a regularity criterion, and then use a bootstrap argument to prove the global well-posedness of strong solutions provided that $\|\rho _0\|_{L^\infty }+\|\nabla d_0\|_{L^6}$ is sufficiently small.
