This paper deals with the 2D incompressible MHD equations with density-dependent viscosity in bounded domain. The global existence of strong solutions are established in the vacuum cases, provided the assumption that \(\bar{\rho }+\|b_{0}\|_{L^{4}}\) is suitably small with large velocity. Furthermore, the exponential decay of the solution is also obtained.

中文翻译：

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具有真空的2D密度相关MHD的全局规律性

本文讨论了在有限域内具有密度依赖粘度的二维不可压缩MHD方程。在真空情况下建立了强解的整体存在性，前提是假设\（\ bar {\ rho} + \ | b_ {0} \ | __L {{4}} \）较小且速度较大。此外，还获得了溶液的指数衰减。