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.
Caffarelli,The smoothness of the free surface in a filtration problem, Archive for Rational Mechanics and Analysis63(1976), no
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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.