The Second Iterate of the Muskat Equation in Supercritical Spaces
Analysis of PDEs
2025-12-29 v1
Abstract
The ill-posedness for the Muskat problem in spaces that are supercritical with respect to the scaling is studied. The main result of the paper establishes that for a sequence of approximations of the Muskat equation obtained via Taylor expansion, their corresponding second Picard's iterate is discontinuous around the origin in a certain family of supercritical spaces approaching a critical space.
Cite
@article{arxiv.2209.04694,
title = {The Second Iterate of the Muskat Equation in Supercritical Spaces},
author = {Esteban Paduro},
journal= {arXiv preprint arXiv:2209.04694},
year = {2025}
}
Comments
29 pages