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

Giovambattista Amendola | Zendy; Mauro Fabrizio | Zendy; John Golden | Zendy; Adele Manes | Zendy

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

Author(s) -

Giovambattista Amendola,

Mauro Fabrizio,

John 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

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