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 | References | Similar Articles | Additional Information
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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Additional Information
Diego Córdoba
Affiliation:
Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Cientificas, Nicolás Cabrera, 13-15, 28059 Madrid, Spain
MR Author ID:
627661
Email:
dcg@icmat.es
Tania Pernas-Castaño
Affiliation:
Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Cientificas, Nicolás Cabrera, 13-15, 28059 Madrid, Spain
MR Author ID:
1007506
Email:
tania.pernas@icmat.es
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