Well-posedness of the Muskat problem with H2 initial data

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

研究成果: 雜誌貢獻期刊論文同行評審

50 引文 斯高帕斯(Scopus)

摘要

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.

原文???core.languages.en_GB???
頁(從 - 到)32-104
頁數73
期刊Advances in Mathematics
286
DOIs
出版狀態已出版 - 2 1月 2016

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