Abstract
We study the compressible magnetohydrodynamic equations in a bounded smooth domain in \({{\mathbb{R}}^2}\) with perfectly conducting boundary, and prove the global existence and uniqueness of smooth solutions around a rest state. Moreover, the low Mach limit of the solutions is verified for all time, provided that the initial data are well prepared.
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Jiang was supported by the National Basic Research Program under the Grant 2011CB309705 and NSFC (Grant No. 11229101), Ju by NSFC (Grant No. 40890154 and 11171035), and Dou by China Postdoctoral Science Foundation (No. 2012M520205).
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Dou, C., Jiang, S. & Ju, Q. Global existence and the low Mach number limit for the compressible magnetohydrodynamic equations in a bounded domain with perfectly conducting boundary. Z. Angew. Math. Phys. 64, 1661–1678 (2013). https://doi.org/10.1007/s00033-013-0311-7
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DOI: https://doi.org/10.1007/s00033-013-0311-7