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Global well-posedness for the incompressible MHD equations with density-dependent viscosity and resistivity coefficients

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Abstract

This paper concerns an initial–boundary value problem of the inhomogeneous incompressible MHD equations in a smooth bounded domain. The viscosity and resistivity coefficients are density-dependent. The global well-posedness of strong solutions is established, provided the initial norms of velocity and magnetic field are suitably small in some sense, or the lower bound of the transport coefficients are large enough. More importantly, there is not any smallness condition on the density and its gradient.

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Authors and Affiliations

  1. School of Applied Mathematics, Xiamen University of Technology, Xiamen, 361024, China

    Xin Si

  2. College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, 330022, China

    Xia Ye

  3. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China

    Xia Ye

Authors
  1. Xin Si
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  2. Xia Ye
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Correspondence to Xia Ye.

Additional information

Supported by the NNSFC (Grant No. 11271306) and the Natural Science Foundation of Fujian Province of China (Grant No. 2015J01023) and the Foundation of Provincial Education Department of China (Grant No. JA15379).

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Si, X., Ye, X. Global well-posedness for the incompressible MHD equations with density-dependent viscosity and resistivity coefficients. Z. Angew. Math. Phys. 67, 126 (2016). https://doi.org/10.1007/s00033-016-0722-3

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  • DOI: https://doi.org/10.1007/s00033-016-0722-3

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