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Global existence, singular solutions, and ill-posedness for the Muskat problem

Abstract:

The Muskat, or Muskat--Leibenzon, problem describes the evolution of the interface between two immiscible fluids in a porous medium or Hele-Shaw cell under applied pressure gradients or fluid injection/extraction. In contrast to the Hele-Shaw problem (the one-phase version of the Muskat problem), there are few nontrivial exact solutions or analytic results for the Muskat problem. For the stable, forward Muskat problem, in which the higher viscosity fluid expands into the lower viscosity flu...

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Michael Siegel More by this author
Russell E. Caflisch More by this author
Sam Howison More by this author
Publication date:
2004
URN:
uuid:4dc6141e-80a6-4eb9-8342-7a8015d383bc
Local pid:
oai:eprints.maths.ox.ac.uk:102

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