Abstract
In this paper, we consider a confined physical scenario to prove the global existence of smooth solutions with bounded density and finite energy for the inviscid incompressible porous media (IPM) equation. The result is proved using the stability of stratified solutions, combined with an additional structure of our initial perturbation, which allows us to get rid of the boundary terms in the energy estimates.
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Acknowledgements
The authors acknowledges helpful conversations with Tarek M. Elgindi. The authors would like to thank the anonymous referee for their insightful comments and suggestions.
Funding
The authors are supported by Spanish National Research Project MTM2014-59488-P and ICMAT Severo Ochoa Projects SEV-2011-0087 and SEV-2015-556, the grant ERC Grant 7882250-NONFLU. AC was partially supported by the ERCGrant 307179-GFTIPFDandDLwas supported by La Caixa-Severo Ochoa grant.
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Communicated by P. Constantin
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Castro, Á., Córdoba, D. & Lear, D. Global Existence of Quasi-Stratified Solutions for the Confined IPM Equation. Arch Rational Mech Anal 232, 437–471 (2019). https://doi.org/10.1007/s00205-018-1324-3
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DOI: https://doi.org/10.1007/s00205-018-1324-3