Energy stability for thermo-viscous fluids with a fading memory heat flux
Giovambattista Amendola - Dipartimento di Matematica, Largo Bruno Pontecorvo 5, Pisa, 56127, Italy (email)
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.
Keywords: Bénard problem, viscous fluid with memory, exponential stability.
Received: April 2015; Revised: July 2015; Available Online: September 2015.
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