Potential theory yields local well-posedness, parabolic smoothing in near-optimal spaces, and exponential stability of equilibria for the capillarity-driven 2D Hele-Shaw problem via a generalized linearized stability principle for abstract quasilinear parabolic equations.
Title resolution pending
3 Pith papers cite this work. Polarity classification is still indexing.
3
Pith papers citing it
citation-role summary
background 1
citation-polarity summary
fields
math.AP 3verdicts
UNVERDICTED 3roles
background 1polarities
background 1representative citing papers
Global well-posedness in strong sense proved for the interface equation of the 2D Hele-Shaw problem with point injection, for arbitrary Lipschitz initial interfaces away from the source.
Global-in-time a priori estimates are proved for the 2D Muskat problem with contact points near equilibrium in non-weighted L2 Sobolev spaces without angle restrictions.
citing papers explorer
-
A potential theory approach to the capillarity-driven Hele-Shaw problem
Potential theory yields local well-posedness, parabolic smoothing in near-optimal spaces, and exponential stability of equilibria for the capillarity-driven 2D Hele-Shaw problem via a generalized linearized stability principle for abstract quasilinear parabolic equations.
-
Global well-posedness for the Hele-Shaw problem with point injection
Global well-posedness in strong sense proved for the interface equation of the 2D Hele-Shaw problem with point injection, for arbitrary Lipschitz initial interfaces away from the source.
-
Global-in-time estimates for the 2D one-phase Muskat problem with contact points
Global-in-time a priori estimates are proved for the 2D Muskat problem with contact points near equilibrium in non-weighted L2 Sobolev spaces without angle restrictions.