Global Well‐Posedness of Incompressible Elastodynamics in Two Dimensions

2016/03/23 by Zhen Lei · 4 citations
Mathematics · Engineering · #Navier-Stokes equation solutions #Advanced Mathematical Physics Problems #Computational Fluid Dynamics and Aerodynamics

paper · doi:10.1002/cpa.21633

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

Cited by

• On the energy method for global well–posedness to 2D simplified inertial Ericksen–Leslie's system near equilibrium
• Global well-posedness for the three dimensional simplified inertial Ericksen-Leslie systems near equilibrium
• Almost global well-posedness of Ericksen-Leslie's hyperbolic liquid crystal model for small data in two dimensions
• Global existence and stability of near-affine solutions of compressible elastodynamics

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\n incompressible viscoelasticity in 3D