三维可压缩磁流体力学方程的重要估计
The Important Estimates for Compressible MHD Equations
DOI: 10.12677/PM.2022.128143, PDF,    国家自然科学基金支持
作者: 王 帅, 陈 菲*, 王传宝：青岛大学，数学与统计学院，山东 青岛
关键词: 频率分解；傅里叶变换；可压缩磁流体力学方程；Frequency Decomposition； Fourier Transform； Compressible Magnetohydrodynamic Equations
摘要: 本文主要研究了三维可压缩磁流体力学方程其线性方程解的重要估计。当频率分别满足|ξ|≤k0和k1≤|ξ|≤k2时，通过傅里叶变换的方法，我们建立了两个重要的估计。从频率分解角度来看，ξ的两个取值范围对应着低频率和中频率，这对于研究三维可压缩磁流体力学非线性方程解的时间衰减率有重要作用。
Abstract: In this paper, the important estimates of solution about linear equations to three-dimensional compressible magnetohydrodynamic equations are mainly studied. By Fourier splitting method, we establish two important estimates in case of the frequency satisfying |ξ|≤k0 and k1≤|ξ|≤k2 respectively. From the perspective of frequency decomposition, the two value ranges of ξ correspond to low frequency and medium frequency, which plays an important role in the study of the time decay rates of solution about nonlinear equations to three-dimensional compressible magnetohydrodynamic equations.
文章引用：王帅, 陈菲, 王传宝. 三维可压缩磁流体力学方程的重要估计[J]. 理论数学, 2022, 12(8): 1305-1311. https://doi.org/10.12677/PM.2022.128143

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