Growth in the Muskat problem
Mathematical modelling of natural phenomena, Tome 15 (2020), article no. 7

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We review some recent results on the Muskat problem modelling multiphase flow in porous media. Furthermore, we prove a new regularity criteria in terms of some norms of the initial data in critical spaces (Ẇ1,∞ and Ḣ3∕2).
DOI : 10.1051/mmnp/2019021

Rafael Granero-Belinchón 1 ; Omar Lazar 2

1 Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria. Avda. Los Castros s/n, Santander, Spain.
2 Departamento de Análisis Matemático & IMUS, Universidad de Sevilla, C/ Tarifa s/n, Campus Reina Mercedes, 41012 Sevilla, Spain.
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Rafael Granero-Belinchón; Omar Lazar. Growth in the Muskat problem. Mathematical modelling of natural phenomena, Tome 15 (2020), article  no. 7. doi: 10.1051/mmnp/2019021

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