Year: 2025
Type: article
Abstract: We derive a PDE that models the behavior of a boundary layer solution to the incompressible porous media (IPM) equation posed on the 2D periodic half-plane. This 1D IPM model is a transport equation with a non-local velocity similar to the well-known Córdoba–Córdoba–Fontelos (CCF) equation. We discuss how this modification of the CCF equation can be regarded as a reasonable model for solutions to the IPM equation. Working in the class of bounded smooth periodic data, we then show local well-posedness for the 1D IPM model as well as finite time blow-up for a class of initial data.
Source: Nonlinearity
Authors: Alexander Kiselev, Naji A Sarsam
Institution: Duke University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W4409956380