Uniqueness and regularity for the 3D Boussinesq system with damping

Thermal convection with generalized friction

“…We have addressed the global nonlinear stability problem for thermal convection with generalized friction in a model recently proposed by [1]. It is shown that the linear instability theory correctly captures the onset of thermal convection by showing that the Rayleigh number threshold for global nonlinear stability employing the energy method is exactly the same as the one obtained by a linear analysis.…”

“…The goal of this paper is to study the stability of the steady conduction solution to the model of [1]. We demonstrate an optimum result in that we show the linear instability threshold for the Rayleigh number coincides with the global nonlinear stability one.…”

“…In a recent paper [1] have proposed a model for thermal convection in a linearly viscous fluid which is subject to a generalized friction term. [1] study the existence and regularity questions for their model.…”