Highly Influenced

# Local Regularization of the One-phase Hele-Shaw Flow

@inproceedings{CHOI2008LocalRO, title={Local Regularization of the One-phase Hele-Shaw Flow}, author={SUNHI CHOI and Inwon Kim}, year={2008} }

- Published 2008

This article presents a local regularity theorem for the one-phase Hele-Shaw flow. We prove that if the Lipschitz constant of the initial free boundary in a unit ball is small, then for small uniform positive time the solution is smooth. This result improves on our earlier results in [CJK] because it is scale-invariant. As a consequence we obtain existence, uniqueness and regularity properties of global solutions with Lipschitz initial free boundary.