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Transactions of the American Mathematical Society

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Non-splat singularity for the one-phase Muskat problem


Authors: Diego Córdoba and Tania Pernas-Castaño
Journal: Trans. Amer. Math. Soc. 369 (2017), 711-754
MSC (2010): Primary 35Q35
DOI: https://doi.org/10.1090/tran6688
Published electronically: April 14, 2016
MathSciNet review: 3557791
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Abstract: For the water wave equations, the existence of splat singularities has been shown, i.e., the interface self-intersects along an arc in finite time. The aim of this paper is to show the absence of splat singularities for the incompressible fluid dynamics in porous media.


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Diego Córdoba
Affiliation: Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Cientificas, Nicolás Cabrera, 13-15, 28059 Madrid, Spain
Email: dcg@icmat.es

Tania Pernas-Castaño
Affiliation: Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Cientificas, Nicolás Cabrera, 13-15, 28059 Madrid, Spain
Email: tania.pernas@icmat.es

DOI: https://doi.org/10.1090/tran6688
Received by editor(s): September 2, 2014
Received by editor(s) in revised form: January 22, 2015
Published electronically: April 14, 2016
Article copyright: © Copyright 2016 American Mathematical Society