三维地核磁流体力学方程组在临界Fourier-Besov 空间中的整体适定性
Global Well-Posedness of theThree-DimensionalMagnetohydrodynamic Equations Arisingfrom the Earth's Core in CriticalFourier-Besov Spaces
DOI: 10.12677/PM.2023.139268, PDF,    科研立项经费支持
作者: 赵丹丹, 孙晋易：西北师范大学，数学与统计学院，甘肃 兰州
关键词: 三维旋转磁流体力学方程组；Fourier-Besov 空间；适定性；Three-Dimensional Magnetohydrodynamics Equations； Global Well-Posedness； Fourier-Besov Spaces
摘要: 三维地核磁流体力学方程组是描述地核中导电金属流体运动与地球磁场变化规律的基本方程组。 通过运用 Littlewood-Paley 分解，并通过建立相应算子半群的一致有界性估计，证明了三维旋转磁流体力学方程组柯西问题关于 Fourier-Besov 空间中小初值的整体适定性。
Abstract: The three-dimensional magnetohydrodynamics equations arising from the Earth's core are the basic equations describing the motion of the conducting metal fluids in the Earth's core and the changes of the Earth's magnetic field. With the help of the Littlewood-Paley decomposition and by establishing the uniformly bounded estimations of the corresponding operator semigroups on Fourier-Besov spaces, we prove the global well-posedness of Cauchy problem of this three-dimensional magnetohydrody-namics equations for small initial data in critical Fourier-Besov spaces.
文章引用：赵丹丹, 孙晋易. 三维地核磁流体力学方程组在临界Fourier-Besov 空间中的整体适定性[J]. 理论数学, 2023, 13(9): 2621-2632. https://doi.org/10.12677/PM.2023.139268

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