Convergence rate estimates for the low Mach and Alfven number three-scale singular limit of compressible ideal Magnetohydrodynamics
Convergence rate estimates for the low Mach and Alfven number three-scale singular limit of compressible ideal Magnetohydrodynamics
复制标题
可压缩理想磁流体动力学低马赫数和阿尔文数三尺度奇异极限的收敛率估计
DOI：
10.1051/m2an/2020051
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通讯作者：
Steve Schochet
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作者：
Bin Cheng;Qiangchang Ju;Steve Schochet
得到了可压缩理想磁流体动力学方程奇异极限的收敛速度估计，其中马赫数和阿尔文数以不同的速度趋于零。证明使用的精确和近似的快速，中间和缓慢的模式与改进的估计的解决方案和它们的时间导数，以及时间积分方法的详细分析。当小参数之间存在幂律关系时，收敛速度是马赫数的正幂，幂随分量和范数的不同而变化。例外的是，两个分量的收敛速度涉及两个参数的比值，并且该速度被证明是sharpviacorrector项。此外，对于小参数之间呈幂律关系的情况，当幂趋于1时，收敛率趋于双尺度收敛率。这些结果表明，三尺度奇异极限的收敛速度问题，这是没有解决的作者的前一份文件，是更复杂的比经典的两尺度奇异极限。
Convergence rate estimates are obtained for singular limits of the compressible ideal magnetohydrodynamics equations, in which the Mach and Alfvén numbers tend to zero at different rates. The proofs use a detailed analysis of exact and approximate fast, intermediate, and slow modes together with improved estimates for the solutions and their time derivatives, and the time-integration method. When the small parameters are related by a power law the convergence rates are positive powers of the Mach number, with the power varying depending on the component and the norm. Exceptionally, the convergence rate for two components involve the ratio of the two parameters, and that rate is proven to be sharpviacorrector terms. Moreover, the convergence rates for the case of a power-law relation between the small parameters tend to the two-scale convergence rate as the power tends to one. These results demonstrate that the issue of convergence rates for three-scale singular limits, which was not addressed in the authors’ previous paper, is much more complicated than for the classical two-scale singular limits.