PACS. 47.20 -Hydrodynamic stability and instability. PACS. 47.25 -Turbulent flows, convection, and heat transfer.Abstract. -The steady convective flow in a compressible fluid layer is computed, for different values of the parameters, using bifurcation theory. We show how to eliminate parasitic 0 eigenvalues due to the Galileian invariance of the problem, and to its partly hyperbolic structure. We compare results with direct numerical simulation, and we discuss the validity on a truncation at the second order in the amplitude for the velocity vector field.
For switching diffusion systems with a homogeneous closed-loop control we establish existence and uniqueness of solution of the equation, and rate of convergence to the stationary regime, as well as mixing rate.
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