Finite time blow-up for the nematic liquid crystal flow in dimension two

2019/08/28 by Chen-Chih Lai, Chen‐Chih Lai, Lai, Chen-Chih +8 · 2 citations
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Navier-Stokes equation solutions #math.AP

paper · pdf · doi:10.48550/arxiv.1908.10955

48pages; any comment is welcome

arxiv created 2019/08/28 · openalex publication_date 2019/08/28 · arxiv updated 2019/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the initial-boundary value problem of a simplified nematic liquid crystal flow in a bounded, smooth domain Ω⊂ \mathbb R². Given any k distinct points in the domain, we develop a new \em inner--outer gluing method to construct solutions which blow up exactly at those k points as t goes to a finite time T. Moreover, we obtain a precise description of the blow-up.

Citations

• Some constitutive equations for liquid crystals
• Sur le mouvement d'un liquide visqueux emplissant l'espace
• Geometry driven Type II higher dimensional blow-up for the critical heat equation

Cited by

• Nematic liquid crystals: Ericksen-Leslie theory with general stress tensors
• From the Landau-de Gennes theory to the Ericksen-Leslie theory in dimension two

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