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Global Existence of Quasi-Stratified Solutions for the Confined IPM Equation

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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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Authors and Affiliations

  1. Instituto de Ciencias Matemáticas (CSIC), C. Nicolás Cabrera, 13-15, 28049, Madrid, Spain

    Ángel Castro, Diego Córdoba & Daniel Lear

Authors
  1. Ángel Castro
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  2. Diego Córdoba
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  3. Daniel Lear
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Corresponding author

Correspondence to Ángel Castro.

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The authors declare that they have no conflict of interest.

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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

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