Córdoba Gazolaz, DiegoGancedo García, Francisco2016-09-212016-09-212007-07Córdoba Gazolaz, D. y Gancedo García, F. (2007). Contour dynamics of incompressible 3-D fluids in a porous medium with different densities. Communications in Mathematical Physics, 273 (2), 445-471.0010-36161432-0916http://hdl.handle.net/11441/45194We 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.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1007/s00220-007-0246-y