Global existence and decay rate of strong solution to incompressible Oldroyd type model equations

This paper investigates the global existence and the decay rate in time of a solution to the Cauchy problem for an incompressible Oldroyd model with a deformation tensor damping term. There are three major results. The first is the global existence of the solution for small initial data. Second, we derive the sharp time decay of the solution in $L^{2}-$norm. Finally, the sharp time decay of the solution of higher order Sobolev norms is obtained.