On the splash and splat singularities for the one-phase inhomogeneous Muskat problem

DOI10.1007/S00332-017-9418-XzbMath1403.35232OpenAlexW2765506631MaRDI QIDQ1631364

Tania Pernas-Castaño, Diego Cordoba

Publication date: 6 December 2018

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00332-017-9418-x

zbMATH Keywords

inhomogeneous Muskat problemfinite-time singularitiesone-phase Muskat problem

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Flows in porous media; filtration; seepage (76S05) Free boundary problems for PDEs (35R35)

Related Items (2)

The multiphase Muskat problem with equal viscosities in two dimensions ⋮ Computer-assisted proofs in PDE: a survey

Cites Work

• On the absence of splash singularities in the case of two-fluid interfaces
• On the impossibility of finite-time splash singularities for vortex sheets
• Splash singularities for the one-phase Muskat problem in stable regimes
• Finite time singularities for the free boundary incompressible Euler equations
• On the finite-time splash and splat singularities for the 3-D free-surface Euler equations
• Local solvability and turning for the inhomogeneous Muskat problem
• Non-splat singularity for the one-phase Muskat problem
• Absence of splash singularities for surface quasi-geostrophic sharp fronts and the Muskat problem
• On turning waves for the inhomogeneous Muskat problem: a computer-assisted proof
• Local-existence for the inhomogeneous Muskat problem
• A pointwise estimate for fractionary derivatives with applications to partial differential equations

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