Global Exponential Nonlinear Stability for Double Diffusive Convection in Porous Medium
Nonlinear stability of the motionless double-diffusive solution of the problem of an infinite horizontal fluid layer saturated porous medium is studied. The layer is heated and salted from below. By introducing two balance fields and through defining new energy functionals it is proved that for CLe ≥ R, Le ≤ 1 the motionless double-diffusive solution is always stable and for CLe < R, Le < 1 the solution is globally exponentially and nonlinearly stable whenever R < 4π2+LeC, where Le, C and R are the Lewis number, Rayleigh number for solute and heat, respectively. Moreover, the nonlinear stability proved here is global and exponential, and the stabilizing effect of the concentration is also proved.
Key wordsenergy method energy functional nonlinear stability diffusive convection porous medium
2010 MR Subject Classification76E06 76E15
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