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

Abstract

We prove that for sufficiently small $H^3$-perturbations of an affine solution, the Cauchy problem for the compressible nonlinear elastodynamics in ${\mathbb{R}}^d$, for $d=2,3$, admits a unique global strong solution. Moreover, we establish the asymptotic behavior of the solution.