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On energy stability for a thermal convection in viscous fluids with memory. (English) Zbl 1343.45012

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.

MSC:

45K05 Integro-partial differential equations
35Q35 PDEs in connection with fluid mechanics
80A17 Thermodynamics of continua
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