GLOBAL SOLUTIONS FOR SOME OLDROYD MODELS OF NON-NEWTONIAN FLOWS

The authors consider here some Oldroyd models of non-Newtonian flows consisting of a strong coupling between incompressible Navier-Stokes equations and some transport equations. It is proved that there exist global weak solutiosn for general initial conditions. The existence proof relies upon showing the propagation in time of the compactness of solutions.