On a class of compressible viscoelastic rate-type fluids with stress--diffusion

TL;DR

This paper develops a mathematical framework for compressible viscoelastic fluids with stress diffusion, extending classical techniques to prove the existence of global weak solutions for finite energy initial data.

Contribution

It introduces new analytical methods, including a modified effective viscous flux identity, to handle the complexities of stress diffusion in compressible viscoelastic fluids.

Findings

Existence of global-in-time weak solutions established.

New version of effective viscous flux identity derived.

Framework applicable to a broad class of fluids with stress diffusion.

Abstract

We develop a mathematical theory for a class of compressible viscoelastic rate-type fluids with stress diffusion. Our approach is based on the concepts used in the nowadays standard theory of compressible Newtonian fluids as renormalization, effective viscous flux identity, compensated compactness. The presence of the extra stress, however, requires substantial modification of these techniques, in particular, a new version of the effective viscous flux identity is derived. With help of these tools, we show the existence of global--in--time weak solutions for any finite energy initial data.