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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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Publication date:
2004-01-01
URN:
uuid:4dc6141e-80a6-4eb9-8342-7a8015d383bc
Local pid:
oai:eprints.maths.ox.ac.uk:102

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