Global strong solution of the 3D compressible liquid crystal flows with density-dependent viscosity and large velocity

Abstract

This paper concerns the Cauchy problem of three-dimensional compressible liquid crystal flows with density-dependent viscosity. When the viscosity coefficients $\hat{I}{¼}_1(\ddot{I}),\hat{I}{¼}_2(\ddot{I})$ are power functions of the density with the power larger than $1$, it is proved that the system exists a unique global strong solution as long as the initial density is sufficiently large and $L^3$-norm of the derivative of the initial director is sufficiently small. This is the first result concerning the global strong solution for three-dimensional compressible liquid crystal flows without smallness of velocity.