Stability of high-temperature viscous flows. A case of pudding model

TL;DR

This paper studies the Navier-Stokes-Fourier system for inhomogeneous heat-conducting fluids, demonstrating the existence of global regular solutions when initial temperature is high, modeling a pudding-like fluid with temperature-dependent viscosity.

Contribution

It establishes the existence of global large solutions for a viscous flow model with temperature-dependent viscosity, a novel result for this class of systems.

Findings

Global regular solutions exist for high initial temperatures.

Viscosity increasing with temperature stabilizes the flow.

The model captures pudding-like fluid behavior.

Abstract

We investigate the Navier-Stokes-Fourier system for incompressible heat conducting inhomogeneous fluid. The main result concerns existence of global in time regular large solutions, provided the initial temperature is sufficiently large. The system may be viewed as a model of pudding, as we assume the viscosity grows with the temperature.