Xinrui Wu, Xingyu Liang
Abstract:
In this article, we establish the existence of unique global solutions for
three-dimensional inhomogeneous incompressible nematic liquid crystal systems.
Our analysis does not assume that the initial density \(\rho_0\) is endowed with any
regularity, requiring only that the fluid density satisfy
\(\|\rho_0-1\|_{L^{\infty}(\mathbb{R}^3)}\leq c\) for a
sufficiently small constant \(c\). While the initial velocity \(u_0\) and the gradient
of the initial molecular orientation \(\nabla \text{d}_0\) belong to the critical space
\(\dot{B}^{-1+\frac{3}{p}}_{p,1}(\mathbb{R}^3)\).
This work extends the result by Danchin and Wang [15]
for the Navier-Stokes equations to the three-dimensional inhomogeneous nematic
liquid crystal system.
Submitted July 18, 2025. Published October 27, 2025.
Math Subject Classifications: 35Q35, 76D03.
Key Words: Inhomogeneous incompressible nematic liquid crystal; critical Besov spaces;
maximal regularity estimates
DOI: 10.58997/ejde.2025.101
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| Xinrui Wu School of Mathematics and Statistics Jiangxi Normal University Nanchang 330022, China email: xinruiwu2001@163.com |
| Xingyu Liang School of Mathematics Nanjing University Nanjing 210093, China email: xingyuliang2000@163.com |
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