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Regularity for the one-phase Hele-Shaw problem from a Lipschitz initial surface. (English) Zbl 1189.35384
Summary: 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.

35R35 Free boundary problems for PDEs
35Q35 PDEs in connection with fluid mechanics
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76D27 Other free boundary flows; Hele-Shaw flows
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