Unconditional nonlinear stability in temperature-dependent viscosity flow in a porous medium

The equations of flow in porous media attributable to Forchheimer are consi dered. In particular, the problem of thermal convection in such a medium is addressed when the viscosity varies with temperature. It is shown that non linear stability may be achieved naturally for all initial data by working with L-3 or L-4 norms, It is also shown that L-2 theory is not sufficient f or such unconditional stability. Previous work has established nonlinear st ability for vanishingly small initial data thresholds, but we believe this is the first analysis that addresses the important physical problem of unco nditional stability. It is shown how to extend the nonlinear analysis for a viscosity linear in temperature to the cases when the viscosity may be qua dratic or when penetrative convection is allowed in the layer.