Pressure jump and radial stationary solutions of the degenerate Cahn-Hilliard equation

Charles Elbar (1) , Benoît Perthame (1) , Jakub Skrzeczkowski (2)

1 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
2 MIMUW - Faculty of Mathematics, Informatics, and Mechanics [Warsaw]

The Cahn-Hilliard equation with degenerate mobility is used in several areas including the modeling of living tissues. We are interested in quantifying the pressure jump at the interface in the case of incompressible flows. To do so, we include an external force and consider stationary radial solutions. This allows us to compute the pressure jump in the small dispersion regime. We also characterize compactly supported stationary solutions in the incompressible case, prove the incompressible limit and prove convergence of the parabolic problems to stationary states.

Mots clés: Asymptotic Analysis; Incompressible limit; Hele-Shaw equations; Surface tension; Pressure jump

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]

Charles Elbar, Benoît Perthame, Jakub Skrzeczkowski. Pressure jump and radial stationary solutions of the degenerate Cahn-Hilliard equation. 2022. ⟨hal-03696545v1⟩