Global smooth solutions for the Cauchy problem in nonlinear viscoelasticity (Q1314625)

We consider the Cauchy problem in three-dimensional nonlinear viscoelasticity for a medium which is homogeneous and initially isotropic. We prove the existence of a global smooth solution for the Cauchy problem in nonlinear viscoelasticity for small data. Moreover we also show that the solution decays as \(t^{-1}\) when \(t\) goes to infinity.