Nonlinear stability of the Muskat problem with capillary pressure at the free boundary

DOI10.1016/S0362-546X(02)00286-9zbMath1028.35123MaRDI QIDQ1868827

Youshan Tao, Avner Friedman

Publication date: 28 April 2003

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

zbMATH Keywords

porous mediumunique global solutionstationary solutionfree boundaryMuskat problemCapillary pressureradially symmetric initial dataincompressible pressuremotion of two immiscible fluids

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Flows in porous media; filtration; seepage (76S05) Free boundary problems for PDEs (35R35) Free-surface potential flows for incompressible inviscid fluids (76B07)

Related Items (19)

The Muskat problem in two dimensions: equivalence of formulations, well-posedness, and regularity results ⋮ On the Muskat problem ⋮ Viscous displacement in porous media: the Muskat problem in 2D ⋮ On a Hele-Shaw flow problem with free and solid boundary components ⋮ Well-posedness and stability results for some periodic Muskat problems ⋮ A note on stability shifting for the Muskat problem ⋮ A new reformulation of the Muskat problem with surface tension ⋮ On a two-phase Hele-Shaw problem with a time-dependent gap and distributions of sinks and sources ⋮ On a two-fluid Hele-Shaw problem with an elliptical interface ⋮ On inverse problems in secondary oil recovery ⋮ Global solutions for a two-phase Hele-Shaw bubble for a near-circular initial shape ⋮ Well-posedness and stability results for a quasilinear periodic Muskat problem ⋮ Analysis of a two-phase model describing the growth of solid tumors ⋮ Free interface evolution in Norton-Hoff flows with numerical aspects ⋮ Exact solutions to a Muskat problem with line distributions of sinks and sources ⋮ The domain of parabolicity for the Muskat problem ⋮ Modelling and analysis of the Muskat problem for thin fluid layers ⋮ The Muskat problem with surface tension and equal viscosities in subcritical \(L_p\)-Sobolev spaces ⋮ Computer-assisted proofs in PDE: a survey

Cites Work

• Equivalent Norms for Sobolev Spaces
• A Stefan problem for a protocell model with symmetry-breaking bifurcations of analytic solutions
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