Global existence with small initial data for three-dimensional incompressible isotropic viscoelastic materials.

摘要

This dissertation contains proof of global existence for a system of nonlinear partial differential equations (PDE) modeling an isotropic incompressible viscoelastic material. 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. As the size of the viscosity approaches zero, we recover a global existence result for an isotropic elastic solid.