Global Low-Energy Weak Solutions of the Equations of Three-Dimensional Compressible Magnetohydrodynamics
Global Low-Energy Weak Solutions of the Equations of Three-Dimensional Compressible Magnetohydrodynamics
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DOI：
10.1007/s00205-012-0498-3
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发表时间：
2012-02
影响因子：
2.5
通讯作者：
Anthony Suen;D. Hoff
中科院分区：
文献类型：
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作者：
Anthony Suen;D. Hoff
我们证明了三维空间中初始数据小，初始密度为正且本质有界的可压缩磁流体动力学方程弱解的整体时间存在性。得到了大量关于部分正则性的信息：速度、涡度和磁场在正时（h1h但notH2）变得相对平滑，压力的奇异性在速度散度的一定倍上抵消了这些奇异性，从而具体表达了从Rankine-Hugoniot条件形式上得到的结论。
We prove the global-in-time existence of weak solutions of the equations of compressible magnetohydrodynamics in three space dimensions with initial data small inL2and initial density positive and essentially bounded. A great deal of information concerning partial regularity is obtained: velocity, vorticity, and magnetic field become relatively smooth in positive time (H1but notH2) and singularities in the pressure cancel those in a certain multiple of the divergence of the velocity, thus giving concrete expression to conclusions obtained formally from the Rankine–Hugoniot conditions.