Localized Mixing Zone for Muskat Bubbles and Turned Interfaces

نویسندگان

چکیده

Abstract We construct mixing solutions to the incompressible porous media equation starting from Muskat type data in partially unstable regime. In particular, we consider bubble and turned interfaces with Sobolev regularity. As a by-product, prove continuation of evolution IPM after Rayleigh–Taylor smoothness breakdown exhibited (Castro et al. Arch Ration Mech Anal 208(3):805–909, 2013, Castro Ann Math. (2) 175(2):909–948, 2012). At each time slice space is split into three evolving domains: two non-mixing zones zone which localized neighborhood region. this way, show compatibility between classical problem convex integration method.

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ژورنال

عنوان ژورنال: Annals of PDE

سال: 2022

ISSN: ['2524-5317', '2199-2576']

DOI: https://doi.org/10.1007/s40818-022-00121-w