1D Model for the 3D Magnetohydrodynamics
1D Model for the 3D Magnetohydrodynamics
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DOI：
10.1007/s00332-023-09944-8
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发表时间：
2021-07
影响因子：
3
通讯作者：
Mimi Dai;Bhakti Vyas;Xiangxiong Zhang
中科院分区：
文献类型：
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作者：
Mimi Dai;Bhakti Vyas;Xiangxiong Zhang
提出了一个三维不可压缩理想磁流体力学的一维模型。对于这个一维模型，建立了局部适定性，并得到了Beale-Kato-Majda型正则性准则。在不考虑拉伸效应的情况下，只考虑输运效应的模型具有整体时间上的强解。一些数值模拟结果表明，具有一定光滑周期初值的模型解在有限时间内不太可能产生奇点，而具有其它初值的模型解则有形成奇点的趋势.
We propose a one-dimensional (1D) model for the three-dimensional (3D) incompressible ideal magnetohydrodynamics. For this 1D model, local well-posedness is established, and a regularity criterion of the Beale–Kato–Majda type is obtained. Without the stretching effect, the model with only transport effect is shown to have global in time strong solution. Some numerical simulations suggest that solutions of the model with certain smooth periodic initial data are not likely to develop singularities in finite time, while solutions starting from other initial data have the tendency to form singularities.