Global strong solution to the 3D incompressible magnetohydrodynamic system in the scaling invariant Besov–Sobolev-type spaces

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• 作者：Haitao Ma ; Xiaoping Zhai ; Wei Yan…
• 关键词：Global strong solution ; MHD system ; Besov spaces
• 刊名：Zeitschrift für angewandte Mathematik und Physik
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：68
• 期：1
• 全文大小：
• 刊物主题：Theoretical and Applied Mechanics; Mathematical Methods in Physics;
• 出版者：Springer International Publishing
• ISSN：1420-9039
• 卷排序：68

文摘

In this paper, we study the global well posedness of the 3D incompressible magnetohydrodynamic system with horizontal dissipation and horizontal magnetic diffusion in the scaling invariant Besov–Sobolev-type spaces. We first get a unique global solution to this system with small initial data by the classical Friedrich’s regularization method. Then using a weighted Chemin–Lerner-type norm, we prove the system also can generate a global solution if the horizontal components of the initial data are small enough compared to the vertical components. In particular, our results imply the global large solutions with highly oscillating initial data.