For initial free boundaries small in H^s with s > d/2 + 1, the one-phase Muskat problem with surface tension has a unique global strong solution that converges to the flat state in Lipschitz norm.
Schwab, Son Tu, and Olga Turanova,Well-posedness for viscosity solutions of the one-phase Muskat problem in all dimensions, Preprint, arXiv:2404.10972 [math.AP] (2024)
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
fields
math.AP 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
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.
citing papers explorer
-
Global well-posedness of the one-phase Muskat problem with surface tension
For initial free boundaries small in H^s with s > d/2 + 1, the one-phase Muskat problem with surface tension has a unique global strong solution that converges to the flat state in Lipschitz norm.
-
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.