Degenerate Two-Phase Incompressible Flow: I. Existence, Uniqueness and Regularity of a Weak Solution

142 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Finite volume approximation for an immiscible two-phase flow in porous media with discontinuous capillary pressure (2013, background): “It is well known that in the case where the domain Ω is homogeneous ([17]), or if x (cid:55)→ π ( s, x ) is a smooth fonction ([7], [18]), then the global pressure belongs to the space L ∞ (0 , T ; H 1 (Ω)).”
Mathematical study of a petroleum-engineering scheme (2003, background): “Note that existence was also shown in [11] for a system taking gravity into account.”
Gradient schemes for two‐phase flow in heterogeneous porous media and Richards equation (2014, background): “The existence of a weak solution to Problem (1), under various hypotheses, is studied in [2, 8, 12, 20] for example.”
Numerical methods for unsaturated flow with dynamic capillary pressure in heterogeneous porous media (2008, methodology): “Furthermore, there exist a plethora of methods applicable to two-phase flow formulation of unsaturated flow, see [25, 43, 22, 23, 21]; however, similarly to the case of Richards’ equation, those results have been formulated for transformed variables or for smooth regime(s).”
Two-phase flow equations with outflow boundary conditions in the hydrophobic–hydrophilic case (2010, background): “Other existence results for the two-phase flow system can be found in [3, 7], regularity results in [8], e.”