We give a sufficient condition for uniqueness for the pressure/saturation system. We establish this condition through analytic arguments, and then construct "mobilities" (or mobility-like functions) that satisfy the new condition (when the parameter is 2). For the constructed "mobilities", we do graphical experiments that show, empirically, that this condition could be satisfied for other values of . These empirical experiments indicate that the usual smoothness condition on the fractional flow function (and on the total mobility), for uniqueness and convergence, might not be necessary. This condition is also sufficient for the convergence of a family of perturbed problems to the original pressure/saturation problem.
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