Abstract
The Muskat problem models the evolution of the interface between two different fluids in porous media. The Rayleigh-Taylor condition is natural to reach linear stability of the Muskat problem. We show that the Rayleigh-Taylor condition may hold initially but break down in finite time. As a consequence of the method used, we prove the existence of water waves turning.
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NOTE={preprint},
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AUTHOR = {Yi, Fahuai},
TITLE = {Global classical solution of {M}uskat free boundary problem},
JOURNAL = {J. Math. Anal. Appl.},
FJOURNAL = {Journal of Mathematical Analysis and Applications},
VOLUME = {288},
YEAR = {2003},
NUMBER = {2},
PAGES = {442--461},
ISSN = {0022-247X},
CODEN = {JMANAK},
MRCLASS = {76S05 (35R35 76D03)},
MRNUMBER = {2019452},
MRREVIEWER = {Li Shang Jiang},
DOI = {10.1016/j.jmaa.2003.09.003},
ZBLNUMBER = {1038.35083},
}