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.
Kim,Uniqueness and existence results on the Hele–Shaw and the Stefan problems, Archive for Rational Mechanics and Analysis168(2003), 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.