  Global existence for a system of nonlinear partial differential equations
(PDE) modeling an isotropic incompressible viscoelastic material is proved. The
structure of the PDE is derived through constitutive assumptions on the
material. Restriction on the size of the initial displacement and velocity for
the model is specified independent of the size of the viscosity of the
material. The proof of global existence combines use of vector fields, local
energy decay estimates, generalized Sobolev inequalities, and hyperbolic energy
estimates.
