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Global large solutions of magnetohydrodynamics with temperature-dependent heat conductivity

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Abstract

In this paper, we consider an initial boundary value problem for the magnetohydrodynamic compressible flows. By assuming that the heat conductivity depends on temperature with κ (θ) = θq, q > 0, we prove the existence and uniqueness of global strong solutions with large initial data and show that neither shock waves nor vacuum and concentration of mass in the solutions are developed in a finite time.

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Authors and Affiliations

  1. Institute of Applied Physics and Computational Mathematics, Beijing, 100088, People’s Republic of China

    Yuxi Hu & Qiangchang Ju

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  1. Yuxi Hu
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  2. Qiangchang Ju
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Correspondence to Yuxi Hu.

Additional information

The second author’s research was supported by the National Basic Research Program (Grant No. 2014CB745000), NSFC (Grant No. 11171035) and BJNSF (Grant No. 1142001).

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Hu, Y., Ju, Q. Global large solutions of magnetohydrodynamics with temperature-dependent heat conductivity. Z. Angew. Math. Phys. 66, 865–889 (2015). https://doi.org/10.1007/s00033-014-0446-1

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  • DOI: https://doi.org/10.1007/s00033-014-0446-1

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