On the Two-Dimensional Muskat Problem with Monotone Large Initial Data

Fan Deng, Zhen Lei, Fang-Hua Lin

Research output: Contribution to journalArticle

Abstract

We consider the evolution of two incompressible, immiscible fluids with different densities in porous media, known as the Muskat problem [21], which in two dimensions is analogous to the Hele-Shaw cell [24]. We establish, for a class of large and monotone initial data, the global existence of weak solutions. The proof is based on a local well-posedness result for the initial data with certain specific asymptotics at spatial infinity and a new maximum principle for the first derivative of the graph function.

Original languageEnglish (US)
JournalCommunications on Pure and Applied Mathematics
DOIs
StateAccepted/In press - 2016

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Maximum principle
Porous materials
Monotone
Derivatives
Immiscible Fluids
Hele-Shaw
Local Well-posedness
Fluids
Existence of Weak Solutions
Maximum Principle
Global Existence
Porous Media
Two Dimensions
Infinity
Derivative
Cell
Graph in graph theory
Class

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

On the Two-Dimensional Muskat Problem with Monotone Large Initial Data. / Deng, Fan; Lei, Zhen; Lin, Fang-Hua.

In: Communications on Pure and Applied Mathematics, 2016.

Research output: Contribution to journalArticle

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