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

Fan Deng, Zhen Lei, Fanghua 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)
Pages (from-to)1115-1145
Number of pages31
JournalCommunications on Pure and Applied Mathematics
Volume70
Issue number6
DOIs
StatePublished - Jun 2017

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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