Global well-posedness is established for the nonlocal interface equation arising from the Hele-Shaw problem with point injection in star-shaped domains with Lipschitz initial data.
$C^1$-Regularity of the Free Boundary for Hele-Shaw Flow with Source and Drift
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
This paper is a continuation of the work in \cite{kimzhang2024} concerning Hele-Shaw flow with both drift and source terms. We prove that, in a local neighborhood, if the free boundary is Lipschitz continuous with a sufficiently small Lipschitz constant, then the free boundary is $C^{1}$. As a corollary, we also consider the 2D vertical Hele-Shaw (or one-phase Muskat) problem with an advection term. We show that, provided the initial data and the advection term are small and the propagation speed is large, the free boundary becomes uniformly $C^1$ after a finite time.
citation-role summary
background 1
citation-polarity summary
fields
math.AP 1years
2026 1verdicts
UNVERDICTED 1roles
background 1polarities
background 1representative citing papers
citing papers explorer
-
Global well-posedness for the Hele-Shaw problem with point injection
Global well-posedness is established for the nonlocal interface equation arising from the Hele-Shaw problem with point injection in star-shaped domains with Lipschitz initial data.