Strong Solutions of Stochastic Models for Viscoelastic Flows of Oldroyd Type

In this work we study stochastic Oldroyd type models for viscoelastic fluids in ${\mathbb{R}}^d,d=2,3$. We show existence and uniqueness of strong local maximal solutions when the initial data are in $H^s$ for $s>d\mathrm{/}2,d=2,3$. 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.