Continuous data assimilation for the 2D magnetohydrodynamic equations using one component of the velocity and magnetic fields
Continuous data assimilation for the 2D magnetohydrodynamic equations using one component of the velocity and magnetic fields
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DOI：
10.3233/asy-171454
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发表时间：
2017-04
期刊：
影响因子：
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通讯作者：
A. Biswas;Joshua Hudson;Adam Larios;Yuan Pei
中科院分区：
文献类型：
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作者：
A. Biswas;Joshua Hudson;Adam Larios;Yuan Pei
针对二维磁流体动力学方程组，提出了几种基于反馈控制的连续数据同化（降尺度）算法。我们表明，对于足够大的控制参数和分辨率的选择，并假设观察到的数据是无误差的，受控系统的解决方案指数收敛（在$L^2$和$H^1$范数）的参考解决方案独立的初始数据选择的受控系统。此外，我们表明，一个类似的结果举行时，控制只放置在水平（或垂直）变量，或在一个单一的Elsasser变量，在更严格的条件下的控制参数和分辨率。最后，利用资料同化系统，我们证明了简化决定模态、节点和体积元的存在性。
We propose several continuous data assimilation (downscaling) algorithms based on feedback control for the 2D magnetohydrodynamic (MHD) equations. We show that for sufficiently large choices of the control parameter and resolution and assuming that the observed data is error-free, the solution of the controlled system converges exponentially (in $L^2$ and $H^1$ norms) to the reference solution independently of the initial data chosen for the controlled system. Furthermore, we show that a similar result holds when controls are placed only on the horizontal (or vertical) variables, or on a single Els\"asser variable, under more restrictive conditions on the control parameter and resolution. Finally, using the data assimilation system, we show the existence of abridged determining modes, nodes and volume elements.