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A degenerate parabolic system for three-phase flows in porous media

Vladimir Shelukhin (2007)

Annales mathématiques Blaise Pascal

A classical model for three-phase capillary immiscible flows in a porous medium is considered. Capillarity pressure functions are found, with a corresponding diffusion-capillarity tensor being triangular. The model is reduced to a degenerate quasilinear parabolic system. A global existence theorem is proved under some hypotheses on the model data.

A differential inclusion : the case of an isotropic set

Gisella Croce (2005)

ESAIM: Control, Optimisation and Calculus of Variations

In this article we are interested in the following problem: to find a map u : Ω 2 that satisfies D u E a.e. in Ω u ( x ) = ϕ ( x ) x Ω where Ω is an open set of 2 and E is a compact isotropic set of 2 × 2 . We will show an existence theorem under suitable hypotheses on ϕ .

A differential inclusion: the case of an isotropic set

Gisella Croce (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this article we are interested in the following problem: to find a map u : Ω 2 that satisfies D u E a.e. in Ω u ( x ) = ϕ ( x ) x Ω where Ω is an open set of 2 and E is a compact isotropic set of 2 × 2 . We will show an existence theorem under suitable hypotheses on φ.

A diffuse interface fractional time-stepping technique for incompressible two-phase flows with moving contact lines

Abner J. Salgado (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

For a two phase incompressible flow we consider a diffuse interface model aimed at addressing the movement of three-phase (fluid-fluid-solid) contact lines. The model consists of the Cahn Hilliard Navier Stokes system with a variant of the Navier slip boundary conditions. We show that this model possesses a natural energy law. For this system, a new numerical technique based on operator splitting and fractional time-stepping is proposed. The method is shown to be unconditionally stable. We present...

A diffused interface whose chemical potential lies in a Sobolev space

Yoshihiro Tonegawa (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We study a singular perturbation problem arising in the scalar two-phase field model. Given a sequence of functions with a uniform bound on the surface energy, assume the Sobolev norms W 1 , p of the associated chemical potential fields are bounded uniformly, where p > n 2 and n is the dimension of the domain. We show that the limit interface as ε tends to zero is an integral varifold with a sharp integrability condition on the mean curvature.

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