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.
@article{arxiv.1402.6605,
title = {Global Well-posedness of Incompressible Elastodynamics in Two Dimensions},
author = {Zhen Lei},
journal= {arXiv preprint arXiv:1402.6605},
year = {2016}
}