Global Well-posedness of Incompressible Elastodynamics in Two Dimensions

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.

To appear in CPAM 2016

References in corpus (5)

• A Priori Estimates for the Free Boundary Problem of Incompressible Neo-Hookean Elastodynamics
• Global well-posedness for the incompressible viscoelastic fluids in the critical $L^p$ framework
• Global existence in critical spaces for incompressible viscoelastic fluids
• Rotation-Strain Decomposition for the Incompressible Viscoelasticity in Two Dimensions
• Almost Global Existence for 2-D Incompressible Isotropic Elastodynamics

Cited by in corpus (1)

• Remarks on Nonlinear Elastic Waves in the Radial Symmetry in 2-D