Well-posedness of the Muskat problem with H2 initial data

C. H.Arthur Cheng, Rafael Granero-Belinchón, Steve Shkoller

Research output: Contribution to journalArticlepeer-review

60 Scopus citations


We study the dynamics of the interface between two incompressible fluids in a two-dimensional porous medium whose flow is modeled by the Muskat equations. For the two-phase Muskat problem, we establish global well-posedness and decay to equilibrium for small H2 perturbations of the rest state. For the one-phase Muskat problem, we prove local well-posedness for H2 initial data of arbitrary size. Finally, we show that solutions to the Muskat equations instantaneously become infinitely smooth.

Original languageEnglish
Pages (from-to)32-104
Number of pages73
JournalAdvances in Mathematics
StatePublished - 2 Jan 2016


  • Free boundary problems
  • Hele-Shaw
  • Moving interfaces
  • Muskat
  • Regularity


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