Degenerate two-phase incompressible flow. II: regularity, stability and stabilization.
The present paper is dedicated to the analysis of a coupled system of highly degenerate elliptic-parabolic partial differential equations for two-phase incompressible flow in porous media. So, is proved that the saturation (unknown \(s\) from the system) is Hölder continuous both in space and time and the total velocity (unknown \(u\) from the system) is Hölder continuous in space (uniformly in time). On the basis of this regularity result, is established next the stability, and the stabilization. Finally, an example is given to show typical regularity of the saturation. For part I, see \textit{Z. Chen}, J. Differ. Equations 171, No. 2, 203--232 (2001; Zbl 0991.35047).
scientific article; zbMATH DE number 1891246