Thermal convection with generalized friction

A model for thermal convection with generalized friction is investigated. It is shown that the linear instability threshold is the same as the global stability one. In addition, decay of the energy in the $$L^2$$ L 2 norm is shown for the perturbation velocity and temperature fields. However, due to the presence of the generalized friction we establish exponential decay in the $$L^{\beta +1}$$ L β + 1 norm for the perturbation temperature, where $$\beta >1$$ β > 1 .

Continuous dependence and convergence for a Kelvin–Voigt fluid of order one

It is shown that the solution to the boundary - initial value problem for a Kelvin–Voigt fluid of order one depends continuously upon the Kelvin–Voigt parameters, the viscosity, and the viscoelastic coefficients. Convergence of a solution is also shown.