This study is concerned with the large time decay rates of the H 1 weak solutions for the 2D magnetohydrodynamic equations with linear damping velocity. Due to the inconsistencies of the dissipative effects between linear velocity and Laplacian magnetic diffusion, neither the classic Fourier splitting method nor Kato’s method is available directly. By developing an alternative analysis argument together with an iterative process, we give a detailed description on the sharp upper decay rates for the velocity field ##IMG## [http://ej.iop.org/images/0951-7715/33/9/4857/nonab8f7dieqn1.gif] {${{\Vert}u\left(t\right){\Vert}}_{{H}^{1}}{\leqslant}C{\left(1+t\right)}^{-\mathrm{min}\left\{1+\gamma ,\;3\right\}}$} and for the magnetic field ##IMG## [http://ej.iop.org/images/0951-7715/33/9/4857/nonab8f7die...] {${{\Vert}b\left(t\right){\Vert}}_{{L}^{2}}{\leqslant}C{\left(1+t\right)}^{-\mathrm{min}\left\{\frac{\gamma }{2},\;1\right\}}$}

中文翻译：

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具有线性阻尼速度的二维MHD方程的H 1弱解的尖锐时间衰减率

这项研究涉及具有线性阻尼速度的二维磁流体动力学方程的H 1弱解的大时间衰减率。由于线速度和拉普拉斯磁扩散之间的耗散效应不一致，因此传统的傅立叶分裂法和加藤法都无法直接使用。通过开发替代分析论证和迭代过程，我们对速度场## IMG ## [http://ej.iop.org/images/0951-7715/33 /9/4857/nonab8f7dieqn1.gif] {$ {{\ Vert} u \ left（t \ right）{\ Vert}} _ {{H} ^ {1}} {\ leqslant} C {\ left（1+ t \ right）} ^ {-\ mathrm {min} \ left \ {1+ \ gamma，\; 3 \ right \}} $}和磁场## IMG ## [http：//ej.iop .org / images / 0951-7715 / 33/9/4857 / nonab8f7die ...