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Global strong solution of the 3D inhomogeneous liquid crystal flows with density-dependent viscosity and large velocity
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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 $\mu(\rho)$ is a power function of the density with the power larger than $1$, that is $\mu(\rho)=\mu\rho^\alpha$ with $\alpha>1$, 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.
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Global strong solution of the 3D compressible liquid crystal flows with density-dependent viscosity and large velocity
For 3D compressible liquid crystal flows with density-dependent viscosity, global strong solutions exist for large initial density and small director gradient, with no smallness condition on velocity.
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