Strong solutions of the compressible nematic liquid crystal flow

2011/04/29 by Tao Huang, Huang, Tao, Changyou Wang +3
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1104.5684

openalex publication_date 2011/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study strong solutions of the simplified Ericksen-Leslie system modeling compressible nematic liquid crystal flows in a domain Ω⊂\mathbb R³. We first prove the local existence of unique strong solutions provided that the initial data ρ₀, u₀, d₀are sufficiently regular and satisfy a natural compatibility condition. The initial density function ρ₀ may vanish on an open subset (i.e., an initial vacuum may exist). We then prove a criterion for possible breakdown of such a local strong solution at finite time in terms of blow up of the quantities ‖ρ‖_L^∞tL^∞x and ‖∇ d‖_L³tL^∞x.

Citations

• A blow-up criterion for the compressible liquid crystals system
• Some constitutive equations for liquid crystals

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