Global Well-posedness for the Three Dimensional Simplified Inertial Ericksen-Leslie Systems Near Equilibrium

2018/01/31 by Yuan Cai, Wei Wang · 24 citations
Mathematics · #Advanced Mathematical Physics Problems #Classical mechanics #Compressibility #Coupling (piping) #Flow (mathematics) #Geometric Analysis and Curvature Flows #Geometry #Inertial frame of reference #Liquid crystal #Mathematical analysis #Mathematics #Mechanics #Navier-Stokes equation solutions #Navier–Stokes equations #Physics #math.AP

paper · pdf · doi:10.1016/j.jfa.2020.108521

published in Journal of Functional Analysis 279(2), 108521 (Elsevier BV) · 30 pages

openalex publication_date 2020/02/20 · arxiv created 2020/03/12 · arxiv updated 2020/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We study a simplified inertial Ericksen-Leslie system for the nematic liquid crystal flow, which can be viewed as a system coupling Navier-Stokes equations and wave map equations. We prove the global existence of classical solution with initial data near equilibrium.

Citations

• On the formation of singularities in the criticalO(3)σ-model
• On almost global existence for nonrelativistic wave equations in 3D
• Weak solutions and development of singularities of the SU(2) σ‐model
• Some constitutive equations for liquid crystals
• The null condition for quasilinear wave equations in two space dimensions I
• Renormalization and blow up for charge one equivariant critical wave maps
• Space‐time estimates for null forms and the local existence theorem
• Liquid crystals with variable degree of orientation
• Conservative Solutions to a System of Variational Wave Equations of Nematic Liquid Crystals
• Global Well‐Posedness of Incompressible Elastodynamics in Two Dimensions

Cited by

• Almost global well-posedness of Ericksen-Leslie's hyperbolic liquid crystal model for small data in two dimensions
• Modeling and Computation of Liquid Crystals
• Global strong solutions to the frame hydrodynamics for biaxial nematic phases
• Poiseuille flow of hyperbolic Ericksen-Leslie system in dimension two

Related

• Global solution to liquid crystal flows in three dimensions
• Global existence of weak solutions of the nematic liquid crystal flow in dimensions three
• Nonexistence of smooth solutions for the general compressible Ericksen -- Leslie equations in three dimensions
• Global well-posedness for the two-dimensional equations of nonhomogeneous incompressible liquid crystal flows with nonnegative density
• Dynamics of the Ericksen-Leslie Equations with General Leslie Stress I: The Incompressible Isotropic Case