The one-phase Hele-Shaw problem with singularities

DOI10.1007/BF02922248zbMath1155.35496OpenAlexW2006013793MaRDI QIDQ816226

Inwon Christina Kim, David S. Jerison

Publication date: 21 February 2006

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: http://www.mathjournals.org/jgan/2005-015-004/2005-015-004-005.html

zbMATH Keywords

cuspsolutionsviscosityfree boundarywedgeHele-Shaw problemfinger-type singularity

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Free boundary problems for PDEs (35R35) Other free boundary flows; Hele-Shaw flows (76D27)

Related Items

Quasistatic droplets in randomly perforated domains, Some free boundary problems recast as nonlocal parabolic equations, The vanishing surface tension limit for the Hele-Shaw problem, The Hele-Shaw problem as a ‘‘Mesa” limit of Stefan problems: Existence, uniqueness, and regularity of the free boundary, An $L^1$ Penalty Method for General Obstacle Problems

Cites Work

• A Harnack inequality approach to the regularity of free boundaries. I: Lipschitz free boundaries are \(C^{1,\alpha}\)
• Regularity of the free boundary in parabolic phase-transition problems
• Uniqueness and existence results on the Hele-Shaw and the Stefan problems
• Regularity of the free boundary for the one phase Hele--Shaw problem
• Cusp Development in Hele–Shaw Flow with a Free Surface
• A Harnack inequality approach to the regularity of free boundaries part II: Flat free boundaries are Lipschitz
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