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Lack of Uniqueness for Weak Solutions of the Incompressible Porous Media Equation

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Abstract

In this work we consider weak solutions of the incompressible two-dimensional porous media (IPM) equation. By using the approach of De Lellis–Székelyhidi, we prove non-uniqueness for solutions in L ∞ in space and time.

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Authors and Affiliations

  1. Instituto de Ciencias Matematicas, Consejo Superior de Investigaciones Cientificas, Calle Serrano 123, 28006, Madrid, Spain

    Diego Cordoba

  2. Department of Mathematics, Instituto de Ciencias Matemáticas, Universidad Autónoma de Madrid, 28049, Madrid, Spain

    Daniel Faraco

  3. Department of Mathematics, University of Chicago, 5734 University Avenue, Chicago, IL, 60637, USA

    Francisco Gancedo

Authors
  1. Diego Cordoba
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  2. Daniel Faraco
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  3. Francisco Gancedo
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Correspondence to Diego Cordoba.

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Communicated by W. E

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Cordoba, D., Faraco, D. & Gancedo, F. Lack of Uniqueness for Weak Solutions of the Incompressible Porous Media Equation. Arch Rational Mech Anal 200, 725–746 (2011). https://doi.org/10.1007/s00205-010-0365-z

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  • DOI: https://doi.org/10.1007/s00205-010-0365-z

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