In this paper we show that if the Lipschitz constant of the initial free boundary is small, then for small positive time the solution is smooth and satisfies the Hele-Shaw equation in the classical sense. A key ingredient in the proof which is of independent interest is an estimate up to order of magnitude of the speed of the free boundary in terms of initial data.
|Original language||English (US)|
|Number of pages||56|
|Journal||American Journal of Mathematics|
|State||Published - Apr 2007|
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