What question did this study set out to answer?

The research focuses on establishing short-time well-posedness for a two-phase fluid flow model through a deformable medium.

April 14, 2026Open Access

Local well-posedness of the Cahn–Hilliard–Biot System

View Full Paper

Ask AI

Bookmark

Authors

Research reveals well-posedness of a fluid flow model in porous media, suggesting stability conditions.

The research focuses on establishing short-time well-posedness for a two-phase fluid flow model through a deformable medium.
Developed a diffuse interface model combining Cahn–Hilliard and Biot's equations.
Addressed solid evolution with phase-field-dependent properties and visco-elastic terms.
Reduced the system to a fixed-point equation for analysis using maximal regularity theory.
Employed a semigroup approach in the absence of visco-elasticity and Banach scales under minimal conditions in its presence.
Short-time well-posedness established for both the visco-elastic and non-visco-elastic cases.
The fixed-point method shows stability for the two-phase fluid flow model.
Reduction strategies showcase different mathematical approaches necessary for varying assumptions.

Abels et al. (2026) studied this question.

View Full Paper

Ask AI

Bookmark