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arXiv · 2609.23760

Global Existence and Large Time Asymptotic Behavior of Strong Solutions to the Two-Dimensional Nematic Liquid Crystal Flows with Large Initial Data and Vacuum

Qinghao Lei·Lu Wang
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Abstract

This paper investigates the two-dimensional nonhomogeneous incompressible nematic liquid crystal flows. For initial density allowed to vanish, we first establish the global existence and exponential decay of strong solutions in bounded domains with density-dependent viscosity, under the assumption that the $L^q$-norm of $\nabla μ(ρ_0)$ is sufficiently small for some $q>2$. As a consequence, we obtain the global existence of strong solutions with large initial data for constant viscosity. Furthermore, for the Cauchy problem with constant viscosity and either vacuum or non-vacuum far-field density, we prove the global existence and large-time decay rates of strong solutions for arbitrarily large initial data. It is worth noting that our results do not require the initial orientation field to satisfy any geometric angle condition.

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Qinghao Lei, Lu Wang. 2026-09-20. Global Existence and Large Time Asymptotic Behavior of Strong Solutions to the Two-Dimensional Nematic Liquid Crystal Flows with Large Initial Data and Vacuum. https://arxiv.org/abs/2609.23760

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