Work

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

Year: 2026

Type: preprint

Abstract: In this paper, we investigate two-dimensional compressible nematic liquid crystal flows with a planar director. We assume that the shear viscosity is a positive constant and that the bulk viscosity is given by $λ(ρ)=ρ^β$ with $β>4/3$. In the periodic domain or in a bounded simply connected smooth domain with Navier-slip and Neumann boundary conditions, we establish the global existence and uniqueness of strong solutions without any restrictions on the size of the initial data. In particular, no geometric angle condition is imposed on the initial orientation field. Moreover, we derive a time-uniform upper bound for the density and establish exponential decay estimates for the strong solutions.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.23764

Authors: Lei, Qinghao, Wang, Lu

Institutions: Chinese Academy of Sciences, Institute of Applied Mathematics, University of Chinese Academy of Sciences, Academy of Mathematics and Systems Science

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7214029510

Cites: 1

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Related to: 10