Global Well-posedness of Incompressible Elastodynamics in Two Dimensions

2014/02/26 by Zhen Lei, Lei, Zhen · 1 citation
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1402.6605

openalex publication_date 2014/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Citations

• On almost global existence for nonrelativistic wave equations in 3D
• The null condition for quasilinear wave equations in two space dimensions I
• Uniform decay estimates and the lorentz invariance of the classical wave equation

Cited by

• Global existence and stability of near-affine solutions of compressible elastodynamics

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