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Contour Dynamics of Incompressible 3-D Fluids in a Porous Medium with Different Densities

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Abstract

We consider the problem of the evolution of the interface given by two incompressible fluids through a porous medium, which is known as the Muskat problem and in two dimensions it is mathematically analogous to the two-phase Hele–Shaw cell. We focus on a fluid interface given by a jump of densities, being the equation of the evolution obtained using Darcy’s law. We prove local well-posedness when the smaller density is above (stable case) and in the unstable case we show ill-posedness.

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Authors and Affiliations

  1. Instituto de Matemáticas y Fisica Fundamental, Consejo Superior de Investigaciones Cientificas, Serrano 123, 28006, Madrid, Spain

    Diego Córdoba & Francisco Gancedo

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  1. Diego Córdoba
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  2. Francisco Gancedo
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Correspondence to Diego Córdoba.

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Communicated by P. Constantin

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Córdoba, D., Gancedo, F. Contour Dynamics of Incompressible 3-D Fluids in a Porous Medium with Different Densities. Commun. Math. Phys. 273, 445–471 (2007). https://doi.org/10.1007/s00220-007-0246-y

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  • DOI: https://doi.org/10.1007/s00220-007-0246-y

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