2009/02/11 by Clément Cancès, Cancès, Clément · 1 citation
Earth and Planetary Sciences · Environmental Science · Mathematics · #35L65 #35L67 #76S05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Geological formations and processes #Methane Hydrates and Related Phenomena #Navier-Stokes equation solutions #math.AP #msc:35L65 #msc:35L67 #msc:76S05
paper · pdf · doi:10.48550/arxiv.0902.1872
openalex publication_date 2009/02/11 · arxiv created 2009/11/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a one-dimensional problem modeling two-phase flow in heterogeneous porous media made of two homogeneous subdomains, with discontinuous capillarity at the interface between them. We suppose that the capillary forces vanish inside the domains, but not on the interface. Under the assumption that the gravity forces and the capillary forces are oriented in opposite directions, we show that the limit, for vanishing diffusion, is not in general the optimal entropy solution of the hyperbolic scalar conservation law as in the first paper of the series \citeNPCX. A non-classical shock can occur at the interface, modeling oil-trapping.