Local regularization of the one-phase hele-shaw flow

Sunhi Choi, David Jerison, K. I.M. Inwon

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

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 [4] because it is scaleinvariant. As a consequence we obtain existence, uniqueness and regularity properties of global solutions with Lipschitz initial free boundary.

Original languageEnglish (US)
Pages (from-to)2765-2804
Number of pages40
JournalIndiana University Mathematics Journal
Volume58
Issue number6
DOIs
StatePublished - Dec 1 2009

Keywords

  • Free boundary
  • Hele-shaw flow
  • Regularity
  • Viscosity solutions

ASJC Scopus subject areas

  • Mathematics(all)

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