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arXiv · 2206.12666

Global regularity of 2D generalized incompressible magnetohydrodynamic equations

Chao Deng·Zhuan Ye·Baoquan Yuan·Jiefeng Zhao
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Abstract

In this paper, we are concerned with the two-dimensional (2D) incompressible magnetohydrodynamic (MHD) equations with velocity dissipation given by $(-\Delta)^{\alpha}$ and magnetic diffusion given by reducing about logarithmic diffusion from standard Laplacian diffusion. More precisely, we establish the global regularity of solutions to the system as long as the power $\alpha$ is a positive constant. In addition, we prove several global \emph{a priori} bounds for the case $\alpha=0$. In particular, our results significantly improve previous works and take us one step closer to a complete resolution of the global regularity issue on the 2D resistive MHD equations, namely, the case when the MHD equations only have standard Laplacian magnetic diffusion.

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Chao Deng, Zhuan Ye, Baoquan Yuan, Jiefeng Zhao. 2022-06-25. Global regularity of 2D generalized incompressible magnetohydrodynamic equations. https://arxiv.org/abs/2206.12666

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