We consider a non-Newtonian incompressible heat conducting fluid with a prescribed nonuniform tem-perature on the boundary and with the no-slip boundary condition for the velocity. We assume no external body forces. For the power-law like models with the power law index bigger than or equal to 11/5 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 proper weak solutions.(c) 2023 Elsevier Inc. All rights reserved.
On the exponential decay in time of solutions to a generalized Navier-Stokes-Fourier system
Abbatiello, A;
2024
Abstract
We consider a non-Newtonian incompressible heat conducting fluid with a prescribed nonuniform tem-perature on the boundary and with the no-slip boundary condition for the velocity. We assume no external body forces. For the power-law like models with the power law index bigger than or equal to 11/5 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 proper weak solutions.(c) 2023 Elsevier Inc. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
