Global Well‐Posedness of Incompressible Elastodynamics in Two Dimensions

2016/03/23 by Zhen Lei · 87 citations
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Cauchy problem #Compressibility #Computational Fluid Dynamics and Aerodynamics #Initial value problem #Isotropy #Mathematical analysis #Mathematics #Mechanics #Navier-Stokes equation solutions #Physics #Sobolev space #Space (punctuation) #Uniqueness

paper · doi:10.1002/cpa.21633

published in Communications on Pure and Applied Mathematics 69(11), 2072-2106 (Wiley)

openalex publication_date 2016/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/25

Abstract

Abstract We prove that for sufficiently small initial displacements in some weighted Sobolev space, the Cauchy problem of the systems of incompressible isotropic Hookean elastodynamics in two space dimensions admits a uniqueness global classical solution. © 2016 Wiley Periodicals, Inc.

Citations

• On almost global existence for nonrelativistic wave equations in 3D
• Almost global existence for 2-D incompressible isotropic elastodynamics
• Uniform decay estimates and the lorentz invariance of the classical wave equation

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• Global existence and stability of near-affine solutions of compressible elastodynamics
• Global Well-posedness of the Incompressible Magnetohydrodynamics
• Small Alfvén Number Limit for the Global-in-time Solutions of Incompressible MHD Equations with General Initial Data

Related

• Global Well-posedness of Incompressible Elastodynamics in Two Dimensions
• Global Well-posedness of Incompressible Elastodynamics in Three Dimensional Thin Domain
• Almost Global Existence for 2-D Incompressible Isotropic Elastodynamics
• Global existence for the 2D incompressible isotropic elastodynamics for small initial data
• Global existence of small displacement solutions for Hookean incompressible viscoelasticity in 3D