Strong solutions of Stochastic models for viscoelastic flows of Oldroyd type

In this work we study stochastic Oldroyd type models for viscoelastic fluids in Rd,d=2,3. We show existence and uniqueness of strong local maximal solutions when the initial data are in Hs for s>d∕2,d=2,3. Probabilistic estimate of the random time interval for the existence of a local solution is expressed in terms of expected values of the initial data.