Unbounded eigenfunctions in the stability problem for a three-layer flow in porous media

Abstract

We study the linear stability of the displacement of three Stokes fluids with constant viscosity in a porous medium when the middle fluid is contained in a bounded region. We use the Hele-Shaw model. The eigenfunctions of the stability system are the amplitudes of the linear perturbations. These amplitudes must be small. We get unbounded eigenfunctions. So the stability problem has no physical sense.