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}
}
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. 

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Showing 1-10 of 16 references

Regularity of free boundary in one phase Hele-Shaw problem

  • I. C. Kim
  • J. Diff
  • 2006

Uniqueness and Existence result of Hele-Shaw and Stefan problem, Arch

  • I. C. Kim
  • Rat. Mech. Anal.,
  • 2003

Persistence of corners in free boundaries in Hele-Shaw flow, Euro

  • J. R. King, A. A. Lacey, J. L. Vazquez
  • J. Appl. Math.,
  • 1995

Regularity of boundaries of quadrature domains in two dimensions

  • M. Sakai
  • SIAM J. Math. Anal,
  • 1993

A Harnack inequality approach to the regularity of free boundaries, Part II: Flat free boundaries are Lipschitz,Comm

  • L. Caffarelli
  • Pure Appl. Math.,
  • 1989

Harnack inequality approach to the regularity of free boundaries , Part II : Flat free boundaries are Lipschitz , Comm

  • I. C. KIM
  • Pure Appl . Math .
  • 1989

A Harnack inequality approach to the regularity of free boundaries, Part I: Lipschitz free boundaries are C1,α, Rev.Mat.Iberoamericana

  • L. Caffarelli
  • 1987

Applications of variational inequalities to a moving boundary problem for Hele Shaw flows, SIAM

  • B. Gustaffson
  • J. Math. Anal.,
  • 1985

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