In this paper, we provide a much simplified proof of the main result in [Lin,Xu, Zhang, arXiv:1302.5877] concerning the global existence and uniqueness ofsmooth solutions to the Cauchy problem for a 2D incompressible viscous andnon-resistive MHD system under the assumption that the initial data are closeto some equilibrium states. Beside the classical energy method, theinterpolating inequalities and the algebraic structure of the equations comingfrom the incompressibility of the fluid are crucial in our arguments. Wecombine the energy estimates with the $L^\infty$ estimates for time slices todeduce the key $L^1$ in time estimates. The latter is responsible for theglobal in time existence.
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机译：在本文中，我们提供了[Lin，Xu，Zhang，arXiv：1302.5877]中关于二维不可压缩粘性和非电阻MHD系统Cauchy问题光滑解的整体存在性和唯一性的主要结果的简化证明。假设初始数据接近某些平衡状态。除了经典的能量方法外，内插不等式和来自流体不可压缩性的方程的代数结构在我们的论证中也至关重要。我们将能量估计与时间片的$ L ^ \ infty $估计相结合，以推断时间估计中的关键$ L ^ 1 $。后者负责时间上的全球存在。
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