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.
Darcy,Les fontaines publiques de la ville de dijon, Dalmont, Paris, 1856
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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.