On hydrodynamics of viscoelastic fluids

In this paper, we study a hydrodynamic system describing fluids with viscoelastic properties. After a brief examination of the relations between several models, we shall concentrate on a few analytical issues concerning them. In particular, we, establish local existence and global existence (with small initial data) of classical solutions for an Oldroyd system without an artificially postulated damping mechanism. (c) 2005 Wiley Periodicals, Inc.