Existence results for a polymer melt with an evolving natural configuration

Abstract

We consider a set of equations governing the behaviour of a polymer melt which is modelled as a viscoelastic fluid possessing a natural, or stress-free state. The natural configuration is characterized through a symmetric, proper orthogonal intermediate deformation tensor, analogous to the left Cauchy-Green deformation tensor in continuum mechanics. This tensor is required to satisfy an evolution equation. It is shown that the constraint that the intermediate tensor be proper orthogonal is satisfied provided that its initial value satisfies this constraint. Local; existence and uniqueness of solutions to the initial boundary value problem of the resulting viscoelastic fluid system are established. It is also shown that the local solutions can be extended globally provided that the data are small enough.