Absence of squirt singularities for the multi-phase Muskat problem

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.

16 pages

References in corpus (1)

• A maximum principle for the Muskat problem for fluids with different densities

Cited by in corpus (11)

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• Regularity results for viscous 3D Boussinesq temperature fronts
• Global well-posedness for the one-phase Muskat problem
• Well-posedness of the Muskat problem with $H^2$ initial data
• Quantitative Hölder Estimates for Even Singular Integral Operators on Patches
• Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves