Local regularization of the one-phase hele-shaw flow

Sunhi Choi, David Jerison, K. I M Inwon

Research output: Contribution to journalArticle

6 Citations (Scopus)

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 - 2009

Fingerprint

Hele-Shaw Flow
Free Boundary
Lipschitz
Regularization
Regularity Properties
Unit ball
Global Solution
Existence and Uniqueness
Regularity
Theorem

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Local regularization of the one-phase hele-shaw flow. / Choi, Sunhi; Jerison, David; Inwon, K. I M.

In: Indiana University Mathematics Journal, Vol. 58, No. 6, 2009, p. 2765-2804.

Research output: Contribution to journalArticle

Choi, Sunhi ; Jerison, David ; Inwon, K. I M. / Local regularization of the one-phase hele-shaw flow. In: Indiana University Mathematics Journal. 2009 ; Vol. 58, No. 6. pp. 2765-2804.
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