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Approximation of the incompressible convective Brinkman–Forchheimer equations

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Abstract

This paper studies the approximation of solutions for the incompressible convective Brinkman–Forchheimer (CBF) equations via the artificial compressibility method. We first introduce a family of perturbed compressible CBF equations that approximate the incompressible CBF equations. Then, we prove the existence and convergence of solutions for the compressible CBF equations to the solutions of the incompressible CBF equations.

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Authors and Affiliations

  1. Department of Mathematics and Information Science, Wenzhou University, Wenzhou, 325035, Zhejiang Province, People’s Republic of China

    Caidi Zhao

  2. Department of Applied Mathematics, Shanghai Normal University, Shanghai, 200234, China

    Yuncheng You

  3. Department of Mathematics and Statistics, University of South Florida, Tampa, FL, 33620, USA

    Yuncheng You

Authors
  1. Caidi Zhao
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  2. Yuncheng You
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Corresponding author

Correspondence to Caidi Zhao.

Additional information

The first author is sponsored by the National NSFC (No.10901121 and 10826091), China postdoctoral Science Foundation (No.20090460952), NSF of Zhejiang Province (No.Y6080077), NSF of Wenzhou University (2008YYLQ01), Zhejiang youth teacher training project and Wenzhou 551 project. The second author is supported in part by NSF Grant DMS-1010998.

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Zhao, C., You, Y. Approximation of the incompressible convective Brinkman–Forchheimer equations. J. Evol. Equ. 12, 767–788 (2012). https://doi.org/10.1007/s00028-012-0153-3

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  • DOI: https://doi.org/10.1007/s00028-012-0153-3

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