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Breakdown of Smoothness for the Muskat Problem

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Abstract

In this paper we show that there exists analytic initial data in the stable regime for the Muskat problem such that the solution turns to the unstable regime and later breaks down, that is, no longer belongs to C 4.

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Authors and Affiliations

  1. Département de Mathématiques et Applications, École Normale Supérieure, 45, Rue d’Ulm, 75005, Paris, France

    Ángel Castro

  2. Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Científicas, Nicolás Cabrera 13-15, 28049, Madrid, Spain

    Diego Córdoba

  3. Department of Mathematics, Princeton University, 1102 Fine Hall, Washington Rd, Princeton, NJ, 08544, USA

    Charles Fefferman

  4. Departamento de Análisis Matemático, Universidad de Sevilla, Tarfia, s/n Campus Reina Mercedes, 41012, Sevilla, France

    Francisco Gancedo

Authors
  1. Ángel Castro
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  2. Diego Córdoba
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  3. Charles Fefferman
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  4. Francisco Gancedo
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Corresponding author

Correspondence to Ángel Castro.

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Communicated by W. E

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Castro, Á., Córdoba, D., Fefferman, C. et al. Breakdown of Smoothness for the Muskat Problem. Arch Rational Mech Anal 208, 805–909 (2013). https://doi.org/10.1007/s00205-013-0616-x

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  • DOI: https://doi.org/10.1007/s00205-013-0616-x

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