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Global strong solution of the 3D inhomogeneous liquid crystal flows with density-dependent viscosity and large velocity https://arxiv.org/abs/2410.11881 #mathAP

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

This paper concerns the initial boundary value problem of three-dimensional inhomogeneous incompressible liquid crystal flows with density-dependent viscosity. When the viscosity coefficient $μ(ρ)$ is a power function of the density with the power larger than $1$, that is $μ(ρ)=μρ^α$ with $α>1$, 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.

arXiv.org
October 18, 2024 at 3:10 AM · · feed2toot · 0 · 0 · 0
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