# Viscoelastic rate type fluids with temperature dependent material parameters -- stability of the rest state

## TL;DR

This paper investigates the stability of the rest state in viscoelastic fluids with temperature-dependent properties, emphasizing the role of thermodynamic analysis in model development.

## Contribution

It demonstrates conditions under which the rest state remains stable, highlighting the importance of thermodynamic considerations in complex fluid models.

## Key findings

- Stable rest state achieved with appropriate material parameters
- Thermodynamic analysis is crucial for model stability
- Provides conditions for stability in temperature-dependent viscoelastic fluids

## Abstract

We study the dynamics of small perturbations to the rest state of a viscoelastic rate type fluid with temperature dependent material parameters. We show that if the material parameters are chosen appropriately, then the quiescent state of the fluid filling an isolated (mechanically, thermally) vessel is a stable state. The outlined analysis explicitly documents the importance of thermodynamic analysis in the development of advanced models for complex fluids.