Global existence of strong solutions with large oscillations and vacuum to the compressible nematic liquid crystal flows in bounded domains with boundaries

Abstract

We investigate compressible nematic liquid crystal flows in three-dimensional (3D) bounded domains with slip boundary condition for velocity and Neumann boundary condition for orientation field. By applying piecewise-estimate method and delicate analysis based on the effective viscous flux and vorticity, we derive the global existence and uniqueness of strong solutions provided that the initial total energy is suitably small. In particular, our result shows that blow up mechanism for local strong solutions obtained by Huang-Wang-Wen (Arch.

A new blowup criterion of strong solutions to the two‐dimensional equations of compressible nematic liquid crystal flows

“…Li et al [5] established the global existence and uniqueness of classical solutions to the Cauchy problem for the isentropic compressible nematic liquid crystal flows in 3D with smooth initial data which are of small energy but possibly large oscillations and vacuum. Later on, Liu and Zhong [6] extend Li et al's result to the initial boundary value problem with slip boundary condition. It should be noted that the 2D case is different from the 3D case when the far field is vacuum.…”