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arXiv · 2209.04694

The Second Iterate of the Muskat Equation in Supercritical Spaces

Esteban Paduro
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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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Esteban Paduro. 2022-09-10. The Second Iterate of the Muskat Equation in Supercritical Spaces. https://doi.org/10.1088/1361-6544/ad2b13

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