Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Liang, Zhengjun
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7160984756
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