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The global well-posedness for the 2D Leray-α MHD equations with zero magnetic diffusivity

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Abstract

By means of Fourier frequency localization and Bony’s paraproduct decomposition, we study the global existence and the uniqueness of the 2D Leray-α Magneta-hydrodynamics model with zero magnetic diffusivity for the general initial data. In view of the profits bring by the α model, then using the energy estimate in the frequency space and the Logarithmic Sobolev inequality, we obtain the estimate \(\int_0^t {{{\left\| {{\nabla _u}} \right\|}_L}\infty ds} \) which is crucial to get the global existence for the general initial data.

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  1. Institute of Applied Physics and Computational Mathematics, P. O. Box 8009, Beijing, 100088, P. R. China

    Qiong Lei Chen

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  1. Qiong Lei Chen
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Correspondence to Qiong Lei Chen.

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Supported by NSF of China (Grant No. 11171034)

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Chen, Q.L. The global well-posedness for the 2D Leray-α MHD equations with zero magnetic diffusivity. Acta. Math. Sin.-English Ser. 32, 1145–1158 (2016). https://doi.org/10.1007/s10114-016-5521-4

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  • DOI: https://doi.org/10.1007/s10114-016-5521-4

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