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Global well-posedness to the 2D Cauchy problem of nonhomogeneous heat conducting magnetohydrodynamic equations with large initial data and vacuum

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Abstract

We establish global well-posedness of strong solutions to the nonhomogeneous heat conducting magnetohydrodynamic equations with non-negative density on the whole space \({\mathbb {R}}^2\). More precisely, under compatibility conditions for the initial data, we show the global existence and uniqueness of strong solutions. Our method relies on delicate energy estimates and a logarithmic interpolation inequality. In particular, the initial data can be arbitrarily large.

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Acknowledgements

The author would like to express his gratitude to the reviewers for careful reading and helpful suggestions which led to an improvement of the original manuscript.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, People’s Republic of China

    Xin Zhong

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  1. Xin Zhong
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Correspondence to Xin Zhong.

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Communicated by Sun-Yung Alice.

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This research was partially supported by National Natural Science Foundation of China (Nos. 11901474, 12071359) and the Innovation Support Program for Chongqing Overseas Returnees (No. cx2020082).

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Zhong, X. Global well-posedness to the 2D Cauchy problem of nonhomogeneous heat conducting magnetohydrodynamic equations with large initial data and vacuum. Calc. Var. 60, 64 (2021). https://doi.org/10.1007/s00526-021-01957-z

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