Continuous dependence and convergence results for Brinkman and Forchheimermodels with variable viscosity

The equations for convective fluid motion in a porous medium of Brinkman or Forchheimer type are analysed when the viscosity varies with either temper ature or a salt concentration. Mundane situations such as salinization requ ire models which incorporate strong viscosity variation. Therefore, we esta blish rigorous a priori bounds with coefficients which depend only on bound ary data, initial data and the geometry of the problem and which demonstrat e continuous dependence of the solution on changes in the viscosity. A conv ergence result is established for the Darcy equations when the variable vis cosity is allowed to tend to a constant viscosity.