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

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


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