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Acta Mathematica Scientia

, Volume 39, Issue 1, pp 119–126 | Cite as

Global Exponential Nonlinear Stability for Double Diffusive Convection in Porous Medium

  • Lanxi Xu (许兰喜)
  • Ziyi Li (李紫奕)
Article

Abstract

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 CLeR, 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 words

energy method energy functional nonlinear stability diffusive convection porous medium 

2010 MR Subject Classification

76E06 76E15 

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Copyright information

© Wuhan Institutes of Physics and Mathematics, Chinese Academy of Sciences 2019

Authors and Affiliations

  1. 1.Department of MathematicsBeijing University of Chemical TechnologyBeijingChina

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