Asymptotic stability of solutions to the Navier-Stokes-Fourier system driven by inhomogeneous Dirichlet boundary conditions

TL;DR

This paper establishes conditions under which solutions to the Navier-Stokes-Fourier system with inhomogeneous boundary data remain bounded over time, advancing understanding of fluid stability far from equilibrium.

Contribution

It introduces a new weak solution concept for the Navier-Stokes-Fourier system with time-dependent boundary conditions and proves their asymptotic stability.

Findings

Global weak solutions are ultimately bounded under certain conditions.

A new weak solution framework accommodates inhomogeneous Dirichlet boundary data.

Results apply to compressible, viscous, heat-conducting fluids far from equilibrium.

Abstract

We consider global in time solutions of the Navier-Stokes-Fourier system describing the motion of a general compressible, viscous and heat conducting fluid far from equilibirum. Using a new concept of weak solution suitable to accommodate the inhomogeneous Dirichlet time dependent data we find sufficient conditions for the global in time weak solutions to be ultimately bounded.