Amendola, Giovambattista; Fabrizio, Mauro; Manes, Adele On energy stability for a thermal convection in viscous fluids with memory. (English) Zbl 1343.45012 Palest. J. Math. 2, No. 2, 144-158 (2013). Summary: Taking into account a new free energy expressed by the minimal state of a viscous fluid with memory, we prove an existence and uniqueness theorem for the related thermal convection problem, defined on arbitrary bounded domains of the three-dimensional space. Some conditions, related with the Rayleigh number, allow us to prove the exponential decay in the linearized problem. Cited in 3 Documents MSC: 45K05 Integro-partial differential equations 35Q35 PDEs in connection with fluid mechanics 80A17 Thermodynamics of continua Keywords:BĂ©nard problem; fluid with memory; exponential stability PDFBibTeX XMLCite \textit{G. Amendola} et al., Palest. J. Math. 2, No. 2, 144--158 (2013; Zbl 1343.45012) Full Text: Link