Energy stability for thermo-viscous fluids with a fading memory heat flux

Giovambattista  Amendola; Mauro  Fabrizio; John Murrough Golden; Adele  Manes

doi:10.3934/eect.2015.4.265

Article Contents

2015, Volume 4, Issue 3: 265-279. Doi: 10.3934/eect.2015.4.265

This issue Previous Article Quasi-stability and global attractor in nonlinear thermoelastic diffusion plate with memory Next Article Null controllability with constraints on the state for the 1-D Kuramoto-Sivashinsky equation

Energy stability for thermo-viscous fluids with a fading memory heat flux

1.
Dipartimento di Matematica, Largo Bruno Pontecorvo 5, Pisa, 56127
2.
Dipartimento di Matematica, Piazza di Porta S. Donato 5, Bologna, 40127
3.
School of Mathematical Sciences, Dublin Institute of Technology, Kevin Street, Dublin 8

Received: April 2015

Revised: July 2015

Published: September 2015

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Abstract

In this work we consider the thermal convection problem in arbitrary bounded domains of a three-dimensional space for incompressible viscous fluids, with a fading memory constitutive equation for the heat flux. With the help of a recently proposed free energy, expressed in terms of a minimal state functional for such a system, we prove an existence and uniqueness theorem for the linearized problem. Then, assuming some restrictions on the Rayleigh number, we also prove exponential decay of solutions.

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Mathematics Subject Classification: Primary: 45K05, 35Q79; Secondary: 80A17, 76D03.

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References

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