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Evolution Equations and Control Theory (EECT)
 

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

Pages: 265 - 279, Volume 4, Issue 3, September 2015      doi:10.3934/eect.2015.4.265

 
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Giovambattista Amendola - Dipartimento di Matematica, Largo Bruno Pontecorvo 5, Pisa, 56127, Italy (email)
Mauro Fabrizio - Dipartimento di Matematica, Piazza di Porta S. Donato 5, Bologna, 40127, Italy (email)
John Murrough Golden - School of Mathematical Sciences, Dublin Institute of Technology, Kevin Street, Dublin 8, Ireland (email)
Adele Manes - 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:  BĂ©nard problem, viscous fluid with memory, exponential stability.
Mathematics Subject Classification:  Primary: 45K05, 35Q79; Secondary: 80A17, 76D03.

Received: April 2015;      Revised: July 2015;      Available Online: September 2015.

 References