三维分数阶MHD-Boussinesq方程组在Besov空间中整体解的存在性
Global Existence of Solutions to the Three-Dimensional MHD-BoussinesqEquations in Besov Spaces
DOI: 10.12677/PM.2025.1511283, PDF,    国家自然科学基金支持
作者: 俞润芝：西北师范大学数学与统计学院，甘肃兰州
关键词: MHD-Boussinesq方程组；Besov空间；整体解；MHD-Boussinesq Equations； Besov Spaces； Global Solutions
摘要: 三维 MHD-Boussinesq方程组描述了导电流体中速度场与磁场相互作用的动力学现象，在地球物理学中有着十分重要的应用。通过建立相应的线性和双线性估计，证明了当初值在Besov空间中满足一定的小性条件时，三维 MHD-Boussinesq方程组存在唯一的整体解。值得一提的是当旋转速度足够快时，允许初始速度任意大。
Abstract: The three-dimensional MHD-Boussinesq equations describe the dynamic phenomena of the interaction between the velocity field and the magnetic field in a conducting fluid, and have very important applications in geophysics. By establishing the corresponding linear and bilinear estimates, we proved that when the initial data sat- isfy certain smallness conditions in the Besov Spaces, the three-dimensional MHD- Boussinesq equations admit a unique global solution. It is worth mentioning that when the rotation speed is sufficiently fast, the initial velocity is allowed to be arbitrarily large.
文章引用：俞润芝. 三维分数阶MHD-Boussinesq方程组在Besov空间中整体解的存在性[J]. 理论数学, 2025, 15(11): 220-232. https://doi.org/10.12677/PM.2025.1511283

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[34] Liu, H., Lin, L. and Sun, C.F. (2025) Global Strong Solution of 3D Temperature-Dependent Incompressible MHD-Boussinesq Equations with Fractional Dissipation. Acta Mathematica Scientia, 45, 418-433.
[35] Wang, Z., Liu, H., Cao, L. and Dong, F. (2025) Global Well-Posedness to the 3-D Inhomogeneous Incompressible MHD-Boussinesq Equations with Vacuum. Zeitschrift fur angewandte Mathematik und Physik, 76, Article No. 115.[CrossRef] 
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