具有磁扩散系数的平面可压缩磁流体动力学方程组密度的上界估计
The Upper Bound of the Density to the Planar Compressible MHD Equations with Magnetic Diffusion Coefficient
DOI: 10.12677/AAM.2023.122082, PDF,   
作者: 王亚茹, 陈恒良：中央民族大学理学院，北京；王建国：北京建筑大学附属中学，北京
关键词: 可压缩磁流体动力学；磁扩散；真空；Compressible Magnetohydrodynamics； Magnetic Diffusion； Vacuum
摘要: 磁流体动力学方程组(MHD)是由Navier-Stokes方程组与Maxwell方程组通过洛伦兹力和欧姆定律耦合而成的偏微分方程组，广泛应用于天体物理、受控热核反应和工业。本文证明了大初值具有磁扩散系数的平面可压缩磁流体动力学方程组初边值问题的密度具有正上界。证明的关键是在大初值的情况下，建立了能量的先验估计，结合方程结构可得到密度的正上界，对求解大初值可压缩磁流体动力学方程初边值问题有重要意义。
Abstract: Magnetohydrodynamic (MHD) equations are partial differential equations which are coupled by Navier-Stokes equations and Maxwell equations through Lorentz force and Ohm’s law. They are widely used in astrophysics, controlled thermonuclear reaction and industry. In this paper, we proved the upper bound of density to the initial boundary value problem of planar compressible magnetohydrodynamics equations with large initial data and magnetic diffusion coefficient. The key of the proof is to establish a priori estimate of the energy in the case of vacuum. It is important to solve the initial boundary value problem of compressible magnetohydrodynamics equation with large initial data.
文章引用：王亚茹, 王建国, 陈恒良. 具有磁扩散系数的平面可压缩磁流体动力学方程组密度的上界估计[J]. 应用数学进展, 2023, 12(2): 801-810. https://doi.org/10.12677/AAM.2023.122082

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