Absence of squirt singularities for the multi-phase Muskat problem

TL;DR

This paper proves that in the multi-phase Muskat problem, involving multiple fluids with different densities in porous media, squirt singularities do not occur during the evolution.

Contribution

The paper establishes the absence of squirt singularities in the multi-phase Muskat problem, providing new mathematical insights into fluid interface stability.

Findings

No formation of squirt singularities in the studied scenario

Enhanced understanding of multi-phase fluid interface behavior

Mathematical proof of singularity absence

Abstract

In this paper we study the evolution of multiple fluids with different constant densities in porous media. This physical scenario is known as the Muskat and the (multi-phase) Hele-Shaw problems. In this context we prove that the fluids do not develop squirt singularities.