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The Second Iterate of the Muskat Equation in Supercritical Spaces

Analysis of PDEs 2025-12-29 v1

Abstract

The ill-posedness for the Muskat problem in spaces that are supercritical with respect to the scaling is studied. The main result of the paper establishes that for a sequence of approximations of the Muskat equation obtained via Taylor expansion, their corresponding second Picard's iterate is discontinuous around the origin in a certain family of supercritical spaces approaching a critical space.

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Cite

@article{arxiv.2209.04694,
  title  = {The Second Iterate of the Muskat Equation in Supercritical Spaces},
  author = {Esteban Paduro},
  journal= {arXiv preprint arXiv:2209.04694},
  year   = {2025}
}

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29 pages