Modelling and analysis of the Muskat problem for thin fluid layers

DOI10.1007/s00021-011-0053-2zbMath1294.76235OpenAlexW1971305715MaRDI QIDQ740346

Bogdan-Vasile Matioc, Joachim Escher, Anca-Voichita Matioc

Publication date: 2 September 2014

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

Full work available at URL: https://doi.org/10.1007/s00021-011-0053-2

zbMATH Keywords

thin layersdegenerate parabolic equationsMuskat problemlinearised stability

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Stability in context of PDEs (35B35) Thin fluid films (76A20) Flows in porous media; filtration; seepage (76S05) Free boundary problems for PDEs (35R35)

Related Items (16)

The porous medium equation as a singular limit of the thin film Muskat problem ⋮ Non-uniform continuity of the semiflow map associated to the porous medium equation ⋮ Bounded weak solutions to the thin film Muskat problem via an infinite family of Liapunov functionals ⋮ Bounded weak solutions to a class of degenerate cross-diffusion systems ⋮ A new reformulation of the Muskat problem with surface tension ⋮ Non-negative global weak solutions for a degenerated parabolic system approximating the two-phase Stokes problem ⋮ Existence result for degenerate cross-diffusion system with application to seawater intrusion ⋮ Surface tension stabilization of the Rayleigh-Taylor instability for a fluid layer in a porous medium ⋮ A thin film approximation of the Muskat problem with gravity and capillary forces ⋮ On the thin film Muskat and the thin film Stokes equations ⋮ Well-posedness of an asymptotic model for capillarity-driven free boundary Darcy flow in porous media in the critical Sobolev space ⋮ On a thin film model with insoluble surfactant ⋮ Self-Similarity in a Thin Film Muskat Problem ⋮ The Muskat problem with surface tension and equal viscosities in subcritical \(L_p\)-Sobolev spaces ⋮ Large time behavior of a two phase extension of the porous medium equation ⋮ Self-similar solutions for the Muskat equation

Cites Work

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• Interface evolution: water waves in 2-D
• Nonlinear stability of the Muskat problem with capillary pressure at the free boundary
• Contour dynamics of incompressible 3-D fluids in a porous medium with different densities
• A generalized Rayleigh–Taylor condition for the Muskat problem
• Thin film equations with soluble surfactant and gravity: Modeling and stability of steady states
• 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
• The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I
• Analytic semigroups and optimal regularity in parabolic problems

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