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

Abstract

This paper concerns the initial boundary value problem of three-dimensional inhomogeneous incompressible liquid crystal flows with density-dependent viscosity. When the viscosity coefficient $\hat{I}¼(\ddot{I})$ is a power function of the density with the power larger than $1$, that is $\hat{I}¼(\ddot{I})=\hat{I}¼\ddot{I}{}^{\hat{I}}\pm$ with $\hat{I}\pm >1$, 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 inhomogeneous liquid crystal flows without smallness of velocity.

27 pages. arXiv admin note: text overlap with arXiv:2408.00333