ABSTRACT
In this paper, the authors study a set of equations which have been proposed by Williams to describe the flow of an incompressible, viscous fluid through a rigid porous medium. Then they consider uniqueness and stability in the case of a saturated body. It will be shown that stability and uniqueness holds for a larger class of initial data than in the Navier-Stokes equations, in particular the people will show that it is possible to have a well-behaved equation with a non-viscous fluid. Existence, uniqueness and stability results valid for the Navier-Stokes system will be shown to hold. It is, however, reasonable to specify the amount of fluid flowing into the body. To examine the effects of viscosity and drag in classical stability the people begin by making the equations dimensionless.
