Global existence, singular solutions, and ill-posedness for the Muskat problem. Siegel, M., Caflisch, R. E., & Howison, S. Comm. Pure Appl. Math., 57(10):1374–1411, 2004.
Global existence, singular solutions, and ill-posedness for the Muskat problem [link]Paper  doi  bibtex   
@article{SCH04,
	Author = {Siegel, Michael and Caflisch, Russel E. and Howison, Sam},
	Doi = {10.1002/cpa.20040},
	Fjournal = {Communications on Pure and Applied Mathematics},
	Issn = {0010-3640},
	Journal = {Comm. Pure Appl. Math.},
	Mrclass = {35Q35 (35R35 76D03 76D27 76S05)},
	Mrnumber = {2070208},
	Mrreviewer = {Alberto Valli},
	Number = {10},
	Pages = {1374--1411},
	Title = {Global existence, singular solutions, and ill-posedness for the {M}uskat problem},
	Url = {https://doi.org/10.1002/cpa.20040},
	Volume = {57},
	Year = {2004},
	Bdsk-Url-1 = {https://doi.org/10.1002/cpa.20040}}

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