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Theory and Applications of Liquid Crystals pp 123–141Cite as

The Flow of Two Immiscible Fluids through a Porous Medium Regularity of the Saturation

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Part of the book series: The IMA Volumes in Mathematics and Its Applications ((IMA,volume 5))

Abstract

We give here a brief account of some recent results obtained jointly with H.W. Alt [2], concerning the regularity of the saturation in the flow of two immiscible fluids through a porous medium.

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References

  1. H.W. Alt and E. DiBenedetto, ‘Non steady flow of water and oil through inhomogeneous porous media’, Ann. Sc. Norm. Sup. Pisa Serie IV Vol. XII no 3 (1985), 335–392.

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  2. H.W. Alt and E. DiBenedetto, Regularity of the saturation in the flow of two immiscible fluids through a porous medium, Centre for Math. Analysis Australian Nat. Univ. Canberra, July 1985.

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  3. E. DiBenedetto, Local behaviour of solutions of degenerate parabolic equations with measurable coefficients, Ann. Sc. Norm. Sup. Pisa (to appear).

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  4. J. Bear, Dynamics of fluids in Porous media, American-Elsevier, New York 1972.

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  5. R.E. Collins, Flow of fluids through Porous Media (3rd ed.) University of Toronto Press, Toronto Ontario, 1974.

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  6. A.E. Scheidegger, The Physics of flow through Porous Media (3rd ed.) Univ. of Toronto Press, Toronto, Ontario, 1974.

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  7. A. Spivak, H.S. Price, A. Settari, Solution of the equations for multidimensional, two-phase immiscible flow by variational methods, Soc. Pet. Eng. J. Feb. 1977, pp. 27–41.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Northwestern University, Evanston, Illinois, 60201, USA

    E. DiBenedetto

Authors
  1. E. DiBenedetto
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Editor information

Editors and Affiliations

  1. Institute for Mathematics and Its Applications, Minneapolis, Minnesota, 55455, USA

    J. L. Ericksen  & David Kinderlehrer  & 

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© 1987 Springer-Verlag New York, Inc.

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DiBenedetto, E. (1987). The Flow of Two Immiscible Fluids through a Porous Medium Regularity of the Saturation. In: Ericksen, J.L., Kinderlehrer, D. (eds) Theory and Applications of Liquid Crystals. The IMA Volumes in Mathematics and Its Applications, vol 5. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8743-5_7

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  • DOI: https://doi.org/10.1007/978-1-4613-8743-5_7

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-8745-9

  • Online ISBN: 978-1-4613-8743-5

  • eBook Packages: Springer Book Archive

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