Regularity for a generalized jeffrey's integral model for viscoelastic fluids

We prove a local existence of a strong solution υ: Ω × T → R3 for a system of nonlinear integrodifferential equations describing motion of an incompressible viscoelastic fluid using standard mathematical tools. The problem is considered in a bounded, smooth domain Ω R3 with a Dirichlet boundary condition and a standard initial condition.