Continuous dependence and convergence results for Brinkman and Forchheimer models with variable viscosity

Abstract

The equations for convective fluid motion in a porous medium of Brinkman or Forchheimer type are analysed when the viscosity varies with either temperature or a salt concentration. Mundane situations such as salinization require models which incorporate strong viscosity variation. Therefore, we establish rigorous a priori bounds with coefficients which depend only on boundary data, initial data and the geometry of the problem, which demonstrate continuous dependence of the solution on changes in the viscosity. A convergence result is established for the Darcy equations when the variable viscosity is allowed to tend to a constant viscosity.