Abstract
This paper is concerned with the global regularity of the 2D (two-dimensional) generalized magnetohydrodynamic equations with only magnetic diffusion \({\Lambda^{2\beta} b}\) . It is proved that when β > 1 there exists a unique global regular solution for this equations. The obtained result improves the previous known ones which require that \({\beta > \frac{3}{2}}\) . With help of Fourier analysis, Besov spaces and singular integral theory, some delicate estimates on the vorticity \({\omega}\) and the current j are established to prove our main result.
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The research is partially supported by National Natural Sciences Foundation of China (Nos. 11171229, 11231006) and Project of Beijing Chang Cheng Xue Zhe.
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Jiu, Q., Zhao, J. Global regularity of 2D generalized MHD equations with magnetic diffusion. Z. Angew. Math. Phys. 66, 677–687 (2015). https://doi.org/10.1007/s00033-014-0415-8
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DOI: https://doi.org/10.1007/s00033-014-0415-8