Dongxiang Chen, Peng Wang
Abstract:
This article concerns the well posedness of solutions for model of a three-dimensional
non-homogeneous incompressible nematic liquid crystal flows with density-dependent
viscosity. We establish the existence of global strong solutions when the initial
data satisfies
\((\rho_0, u_0, \nabla d_0)\in L^\infty(\mathbb{R}^3)
\times \dot{H}^{1/2}(\mathbb{R}^3)\times \dot{H}^{1/2}(\mathbb{R}^3)\),
and uniqueness when
\((\rho_0, u_0,\nabla d_0)\in \dot{B}_{q,1}^{3/q}(\mathbb{R}^3)
\times \dot{B}_{2,1}^{1/2}(\mathbb{R}^3)\times \dot{B}_{2,1}^{1/2}(\mathbb{R}^3)\).
These results refines the corresponding results obtained by Ye and Zhang [23]
Submitted November 4, 2025. Published March 25, 2026.
Math Subject Classifications: 35Q35, 76D03.
Key Words: Inhomogeneous incompressible liquid crystal flow; well-posedness;
density-dependent viscosity; critical Sobolev space.
DOI: 10.58997/ejde.2026.23
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| Dongxiang Chen School of Mathematics and Statistics Jiangxi Normal University Nan Chang 330022, China email: chendx@163.com |
|
Peng Wang School of Mathematics and Statistics Jiangxi Normal University Nan Chang 330022, China email: wangpeng1739@163.com |
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