A Maximum Principle for the Muskat Problem for Fluids with Different Densities |
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| Authors: | Diego Córdoba and Francisco Gancedo |
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| Institution: | (1) Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Científicas, Serrano 123, 28006 Madrid, Spain;(2) Department of Mathematics, University of Chicago, 5734 University Avenue, Chicago, IL 60637, USA |
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| Abstract: | We study the fluid interface problem given by two incompressible fluids with different densities evolving by Darcy’s law.
This scenario is known as the Muskat problem for fluids with the same viscosities, being in two dimensions mathematically
analogous to the two-phase Hele-Shaw cell. We prove in the stable case (the denser fluid is below) a maximum principle for
the L
∞ norm of the free boundary. |
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| Keywords: | |
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