Córdoba Gazolaz, Diego; Granero-Belinchón, Rafael; Orive-Illera, Rafael The confined Muskat problem: differences with the deep water regime. (English) Zbl 1301.35102 Commun. Math. Sci. 12, No. 3, 423-455 (2014). Summary: We study the evolution of the interface given by two incompressible fluids with different densities in the porous strip. This problem is known as the Muskat problem and is analogous to the two phase Hele-Shaw cell. The main goal of this paper is to compare the qualitative properties between the model when the fluids move without boundaries and the model when the fluids are confined. We find that, in a precise sense, the boundaries decrease the diffusion rate and the system becomes more singular. Cited in 25 Documents MSC: 35Q35 PDEs in connection with fluid mechanics 35R35 Free boundary problems for PDEs 76D27 Other free boundary flows; Hele-Shaw flows 76S05 Flows in porous media; filtration; seepage 76T99 Multiphase and multicomponent flows 35B50 Maximum principles in context of PDEs 35B44 Blow-up in context of PDEs Keywords:Darcy’s law; Hele-Shaw cell; Muskat problem; maximum principle; well-posedness; blow-up; ill-posedness PDFBibTeX XMLCite \textit{D. Córdoba Gazolaz} et al., Commun. Math. Sci. 12, No. 3, 423--455 (2014; Zbl 1301.35102) Full Text: DOI arXiv