Nonuniqueness of Steady State Fingering Solutions in Porous Media
James E. Varnon, Robert A. Greenkorn · Water Resources Research · 1970
Steady state solutions for single viscous fingers are nonunique because the position of the interfacial boundary is not specified. Expanding the steady state problem to include an arbitrary number of fingers does not make the solution unique. The initial value problem however does have a unique solution, which suggests that it is futile to look for additional conservation type equations in the hope of making the steady state solutions unique.