# Strong Solutions of Stochastic Models for Viscoelastic Flows of Oldroyd Type

## TL;DR

This paper establishes the existence and uniqueness of strong local solutions for stochastic Oldroyd models of viscoelastic fluids in two and three dimensions, with probabilistic estimates based on initial data.

## Contribution

It provides the first rigorous proof of strong solutions for stochastic Oldroyd models with initial data in Sobolev spaces, including probabilistic estimates of solution existence times.

## Key findings

- Existence and uniqueness of strong local solutions in 2D and 3D.
- Probabilistic estimates for the lifespan of solutions.
- Solutions depend continuously on initial data.

## Abstract

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 $s>d/2, d= 2, 3$. 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.