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Incompressible limit of ideal magnetohydrodynamics in a domain with boundaries

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Abstract

We study the incompressible limit of classical solutions to compressible ideal magneto-hydrodynamics in a domain with a flat boundary. The boundary condition is characteristic and the initial data is general. We first establish the uniform existence of classical solutions with respect to the Mach number. Then, we prove that the solutions converge to the solution of the incompressible MHD system. In particular, we obtain a stronger convergence result by using the dispersion of acoustic waves in the half space.

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Acknowledgements

Jiawei Wang wishes to thank Dr. Biyi Wang and Dr. Ang Li from the Institute of Applied Physics and Computational Mathematics for their valuable advice on the physical background and initial-boundary problems of the MHD system.

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Authors and Affiliations

  1. Institute of Applied Physics and Computational Mathematics, Beijing, 100088, China

    Qiangchang Ju & Jiawei Wang

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  1. Qiangchang Ju
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  2. Jiawei Wang
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Correspondence to Jiawei Wang.

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Conflict of Interest The authors declare no conflict of interest.

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This work was supported by the NSFC (12131007, 12071044).

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Ju, Q., Wang, J. Incompressible limit of ideal magnetohydrodynamics in a domain with boundaries. Acta Math Sci 44, 1441–1465 (2024). https://doi.org/10.1007/s10473-024-0414-6

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  • DOI: https://doi.org/10.1007/s10473-024-0414-6

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