Open AccessEnergy stability for thermo-viscous fluids with a fading memory heat flux
Author(s) -
Giovambattista Amendola,
Mauro Fabrizio,
John M. Golden,
Adele Manes
Publication year - 2015
Publication title -
evolution equations and control theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 19
eISSN - 2163-2480
pISSN - 2163-2472
DOI - 10.3934/eect.2015.4.265
Subject(s) - uniqueness , heat flux , compressibility , work (physics) , physics , space (punctuation) , energy (signal processing) , mechanics , mathematical analysis , thermodynamics , heat transfer , mathematics , computer science , quantum mechanics , operating system
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