On the incompressible limits for the full magnetohydrodynamics flows
On the incompressible limits for the full magnetohydrodynamics flows
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DOI：
10.1016/j.jde.2011.04.016
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发表时间：
2011-10
影响因子：
2.4
通讯作者：
Young-Sam Kwon;K. Trivisa
中科院分区：
文献类型：
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作者：
Young-Sam Kwon;K. Trivisa
本文建立了磁流体动力学流动控制方程在有界和无界区域上弱解的不可压缩极限。磁流体动力学流动的控制方程由完整的Navier-Stokes系统表示，该系统适用于由于磁场和重力的存在而增强的可压缩流体，并带有描述磁场演化的附加方程。磁流体动力学控制方程的尺度类比包括马赫数、弗劳德数和阿尔芬数。在有界域的情况下，奇异极限的建立依赖于声学算子特征值的详细分析，而无界域的情况是通过有界域族的适当逼近和一致边界的推导来处理的。
In this article the incompressible limits of weak solutions to the governing equations for magnetohydrodynamics flows on both bounded and unbounded domains are established. The governing equations for magnetohydrodynamic flows are expressed by the full Navier–Stokes system for compressible fluids enhanced by forces due to the presence of the magnetic field as well as the gravity and with an additional equation which describes the evolution of the magnetic field. The scaled analogues of the governing equations for magnetohydrodynamic flows involve the Mach number, Froude number and Alfven number. In the case of bounded domains the establishment of the singular limit relies on a detail analysis of the eigenvalues of the acoustic operator, whereas the case of unbounded domains is being treated by their suitable approximation by a family of bounded domains and the derivation of uniform bounds.