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.
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math.AP 2years
2026 2verdicts
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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
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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.
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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.