Global well-posedness for the Hele-Shaw problem with point injection
Analysis of PDEs
2026-05-29 v2
Abstract
We study the two-dimensional Hele-Shaw problem with point injection for star-shaped domains. We reduce the system to a nonlocal parabolic equation of the interface, and for arbitrary Lipschitz initial interface away from the source, we prove global well-posedness of the interface equation in a strong sense. We also introduce a viscosity-solution framework for the interface equation and relate it to the classical viscosity theory for the Hele-Shaw problem.
Keywords
Cite
@article{arxiv.2605.11251,
title = {Global well-posedness for the Hele-Shaw problem with point injection},
author = {Zhengjun Liang},
journal= {arXiv preprint arXiv:2605.11251},
year = {2026}
}
Comments
55 pages, 2 figures. Improved exposition and corrected some non-structural errors