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Incompressible Limit of the Compressible Magnetohydrodynamic Equations with Periodic Boundary Conditions

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Abstract

This paper is concerned with the incompressible limit of the compressible magnetohydrodynamic equations with periodic boundary conditions. It is rigorously shown that the weak solutions of the compressible magnetohydrodynamic equations converge to the strong solution of the viscous or inviscid incompressible magnetohydrodynamic equations as long as the latter exists both for the well-prepared initial data and general initial data. Furthermore, the convergence rates are also obtained in the case of the well-prepared initial data.

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Authors and Affiliations

  1. LCP, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing, 100088, P.R. China

    Song Jiang

  2. Institute of Applied Physics and Computational Mathematics, P.O. Box 8009-28, Beijing, 100088, P.R. China

    Qiangchang Ju

  3. Department of Mathematics, Nanjing University, Nanjing, 210093, P.R. China

    Fucai Li

Authors
  1. Song Jiang
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  2. Qiangchang Ju
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  3. Fucai Li
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Correspondence to Fucai Li.

Additional information

Communicated by P. Constantin

Dedicated to Professor Ling Hsiao on the occasion of her 70th birthday.

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Jiang, S., Ju, Q. & Li, F. Incompressible Limit of the Compressible Magnetohydrodynamic Equations with Periodic Boundary Conditions. Commun. Math. Phys. 297, 371–400 (2010). https://doi.org/10.1007/s00220-010-0992-0

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  • DOI: https://doi.org/10.1007/s00220-010-0992-0

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