On the existence of solutions to the Muskat problem with surface tension

DOI10.1007/s00021-016-0297-yzbMath1386.35358OpenAlexW2521227582MaRDI QIDQ1690456

Spencer Tofts

Publication date: 19 January 2018

Published in: Journal of Mathematical Fluid Mechanics (Search for Journal in Brave)

Full work available at URL: https://repository.upenn.edu/cgi/viewcontent.cgi?article=3844&context=edissertations

zbMATH Keywords

uniquenesslocal existencesurface tensionglobal existenceMuskat

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35)

Related Items (8)

The Muskat problem in two dimensions: equivalence of formulations, well-posedness, and regularity results ⋮ Well-posedness of the Muskat problem in subcritical L_p-Sobolev spaces ⋮ Viscous displacement in porous media: the Muskat problem in 2D ⋮ Well-posedness and stability results for some periodic Muskat problems ⋮ A new reformulation of the Muskat problem with surface tension ⋮ Well-posedness and stability results for a quasilinear periodic Muskat problem ⋮ The Muskat problem with surface tension and equal viscosities in subcritical \(L_p\)-Sobolev spaces ⋮ Growth in the Muskat problem

Cites Work

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• Interface evolution: the Hele-Shaw and Muskat problems
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• A maximum principle for the Muskat problem for fluids with different densities
• Well-posedness of the Muskat problem with \(H^2\) initial data
• A center manifold analysis for the Mullins-Sekerka model
• Classical solutions for Hele-Shaw models with surface tension
• On the global existence for the Muskat problem
• The zero surface tension limit of two-dimensional interfacial Darcy flow
• Contour dynamics of incompressible 3-D fluids in a porous medium with different densities
• Breakdown of smoothness for the Muskat problem
• Vorticity and Incompressible Flow
• On the Muskat problem: Global in time results in 2D and 3D
• A generalized Rayleigh–Taylor condition for the Muskat problem
• Global existence, singular solutions, and ill-posedness for the Muskat problem
• The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid

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