Local existence and uniqueness of solutions for non stationary compressible viscoelastic fluid of Oldroyd type

TL;DR

This paper proves the local existence and uniqueness of solutions for a compressible viscoelastic fluid modeled by Oldroyd-B equations within a bounded domain, using a fixed point approach.

Contribution

It establishes the local well-posedness of the compressible Oldroyd-B model, which was previously unproven for this setting.

Findings

Proved local existence of solutions.

Established uniqueness of solutions.

Applied fixed point method for proof.

Abstract

This work is devoted to the study of a compressible viscoelastic fluids satisfying the Oldroyd-B model in a regular bounded domain. We prove the local existence of solutions and uniqueness of flows by a classical fixed point argument.