Mathematical Analysis of Viscoelastic Fluids of White-Metzner Type

This work is concerned with the study of the flow of an incompressible viscoelastic fluid of White-Metzner type. Because of the dependence of the viscosity and relaxation functions on the second invariant of the rate of deformation tensor, this model leads to a nonlinear (not quasilinear) partial differential equations system. We establish several results on the existence, uniqueness, and stability of solutions of the 2-D initial boundary value problem.