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arXiv · 2505.11206

Global Regularity to the liquid crystal flows of Q-tensor model

Z. Chen·E. Terraneo
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Abstract

In this paper we investigate a forced incompressible Navier-Stokes equation coupled with a parabolic type equation of Q-tensors in a domain $U\subset\R^3.$ In the case $U$ is bounded, we prove the existence of a global strong solution when the initial data are sufficiently small, improving a result in Xiao's paper [J. Differ. Equations 2017]. The key tool of the proof is a {maximum principle.} Then, we establish also a result of continuous dependence of solutions on the initial data. Finally, if $U=\R^3,$ based on a result of Du, Hu and Wang [Arch. Rational Mech. Anal. 2020], we give an interesting regularity criterium just via the $\dot{B}^{-1}_{\infty,\infty}$ norm of $u$ and the $L^\infty$ norm of the initial data $Q_0$.

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Z. Chen, E. Terraneo. 2025-05-16. Global Regularity to the liquid crystal flows of Q-tensor model. https://arxiv.org/abs/2505.11206

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