On the exponential decay in time of solutions to a~generalized Navier-Stokes-Fourier system
Analysis of PDEs
2022-10-21 v1
Abstract
We consider a non-Newtonian incompressible heat conducting fluid with prescribed nonuniform temperature on the boundary and with the no-slip boundary conditions for the velocity. We assume no external body forces. For the power-law like models with the power law index bigger than in three dimensions, we identify a class of solutions fulfilling the entropy equality and converging to the equilibria exponentially in a proper metric. In fact, we show the existence of a Lyapunov functional for the problem. Consequently, the steady solution is nonlinearly stable and attracts all suitable weak solutions.
Keywords
Cite
@article{arxiv.2210.10878,
title = {On the exponential decay in time of solutions to a~generalized Navier-Stokes-Fourier system},
author = {Anna Abbatiello and Miroslav Bulíček and Petr Kaplický},
journal= {arXiv preprint arXiv:2210.10878},
year = {2022}
}