Exact boundary controllability for the ideal magneto-hydrodynamic equations
Exact boundary controllability for the ideal magneto-hydrodynamic equations
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DOI：
10.1016/j.jde.2022.02.022
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发表时间：
2021-08
影响因子：
2.4
通讯作者：
I. Kukavica;Matthew Novack;V. Vicol
中科院分区：
文献类型：
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作者：
I. Kukavica;Matthew Novack;V. Vicol
我们通过在侧边界上规定控制来解决矩形域中 MHD 系统的可控性问题。我们确定数据是零可控的充分必要条件，即可以被驱动到零状态。我们还表明，该条件的有效性允许状态相互搅拌。如果不满足条件，则可以借助简单的剪切外磁力从一种状态移动到另一种状态。
We address the problem of controllability of the MHD system in a rectangular domain with a control prescribed on the side boundary. We identify a necessary and sufficient condition on the data to be null-controllable, i.e., can be driven to the zero state. We also show that the validity of this condition allows the states to be stirred to each other. If the condition is not satisfied, one can move from one state to another with the help of a simple shear external magnetic force.