Localized Mixing Zone for Muskat Bubbles and Turned Interfaces
EntityUAM. Departamento de Matemáticas
10.1007/s40818-022-00121-wAnnals of PDE 8 (2022): 7
ISSN2524-5317 (print); 2199-2576 (online)
Funded byAC, DF and FM are supported by grants SEV2015-0554, CEX2019-000904-S and RED2018-102650-T funded by: MCIN/AEI/ 10.13039/501100011033. AC is supported by grants Europa Excelencia program ERC2018-092824, MTM2017-89976-P and PID2020-114703GB-I00 funded by: MCIN/AEI/ 10.13039/501100011033. DF is partially supported by the Line of excellence for University Teaching Staff between CM and UAM. DF and FM are partially supported by the ERC Advanced Grant 834728 and by the MTM2017-85934-C3-2-P
ProjectGobierno de España. MCIN/AEI/ 10.13039/501100011033; Gobierno de España. ERC2018-092824; Gobierno de España. PID2020-114703GB-I00
Rights© The Author(s) 2022
Esta obra está bajo una Licencia Creative Commons Atribución 4.0 Internacional.
We construct mixing solutions to the incompressible porous media equation starting from Muskat type data in the partially unstable regime. In particular, we consider bubble and turned type interfaces with Sobolev regularity. As a by-product, we prove the continuation of the evolution of IPM after the Rayleigh–Taylor and smoothness breakdown exhibited in (Castro et al. in Arch Ration Mech Anal 208(3):805–909, 2013, Castro et al. in Ann Math. (2) 175(2):909–948, 2012). At each time slice the space is split into three evolving domains: two non-mixing zones and a mixing zone which is localized in a neighborhood of the unstable region. In this way, we show the compatibility between the classical Muskat problem and the convex integration method
Files in this item
This item appears in the following Collection(s)
Showing items related by title, author, creator and subject.