| Issue |
Math. Model. Nat. Phenom.
Volume 15, 2020
Growth phenomena
|
|
|---|---|---|
| Article Number | 7 | |
| Number of page(s) | 23 | |
| DOI | https://doi.org/10.1051/mmnp/2019021 | |
| Published online | 17 February 2020 | |
Growth in the Muskat problem*
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.
** Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
9
October
2018
Accepted:
25
April
2019
Abstract
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).
Mathematics Subject Classification: 35A01 / 35D30 / 35D35 / 35Q35 / 35Q86
Key words: Fluid interface / Muskat equation / global strong solution / regularity criteria
Both R.G-B. and O.L. were supported by the National Grant MTM2014-59488-P from the Spanish government and ICMAT Severo Ochoa project SEV-2015-55. O.L. was supported by the ERC through the Starting Grant project H2020-EU.1.1.-63922.
© EDP Sciences, 2020
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