The second iterate of the Muskat equation in supercritical spaces

Author:

Paduro EstebanORCID

Abstract

Abstract The ill-posedness of the Muskat problem in spaces that are supercritical with respect to scaling is studied. The paper’s main result 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.

Funder

Agencia Nacional de Investigación y Desarrollo

Publisher

IOP Publishing

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