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.

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

AMENDOLA, GIOVAMBATTISTA;MANES, ADELE
2015

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.
Amendola, Giovambattista; Fabrizio, Mauro; Golden, John Murrough; Manes, Adele
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/762898
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