Well-posedness for viscosity solutions of the one-phase Muskat problem in all dimensions
Analysis of PDEs
2025-05-05 v4
Abstract
In this article, we apply the viscosity solutions theory for integro-differential equations to the \emph{one-phase} Muskat equation (also known as the Hele-Shaw problem with gravity). We prove global well-posedness for the corresponding Hamilton-Jacobi-Bellmann equation with bounded, uniformly continuous initial data, in all dimensions.
Keywords
Cite
@article{arxiv.2404.10972,
title = {Well-posedness for viscosity solutions of the one-phase Muskat problem in all dimensions},
author = {Russell Schwab and Son Tu and Olga Turanova},
journal= {arXiv preprint arXiv:2404.10972},
year = {2025}
}
Comments
41 pages. Updated Section 5