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Global well-posedness of the 3D Boussinesq-MHD system without heat diffusion

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Abstract

In this paper, we show the global existence and uniqueness of strong and smooth large solutions to the 3D Boussinesq-MHD system without heat diffusion. Since the temperature satisfies a transport equation, in order to get high regularity of temperature, we need to use the combination of estimates about velocity and magnetic field. Moreover, our system involves a nonlinear damping term in the momentum equations due to the Brinkman–Forchheimer–extended-Darcy law of flow in porous media.

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Acknowledgements

The second author D. Bian was partially supported by NSFC under the contracts 11871005 and 11771041. The third author X. Pu was partially supported by NSFC under the contract 11871172.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China

    Huimin Liu

  2. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, China

    Dongfen Bian

  3. Division of Applied Mathematics, Brown University, Providence, RI, 02912, USA

    Dongfen Bian

  4. Department of Mathematics, Chongqing University, Chongqing, 401331, China

    Xueke Pu

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  1. Huimin Liu
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  2. Dongfen Bian
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  3. Xueke Pu
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Correspondence to Dongfen Bian.

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Liu, H., Bian, D. & Pu, X. Global well-posedness of the 3D Boussinesq-MHD system without heat diffusion. Z. Angew. Math. Phys. 70, 81 (2019). https://doi.org/10.1007/s00033-019-1126-y

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  • DOI: https://doi.org/10.1007/s00033-019-1126-y

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