Dissipative solutions and the incompressible inviscid limits of the compressible magnetohydrodynamic system inunbounded domains
Dissipative solutions and the incompressible inviscid limits of the compressible magnetohydrodynamic system inunbounded domains
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DOI：
10.3934/dcds.2014.34.121
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发表时间：
2013-06
影响因子：
1.1
通讯作者：
E. Feireisl;A. Novotný;Yongzhong Sun
中科院分区：
文献类型：
--
作者：
E. Feireisl;A. Novotný;Yongzhong Sun
我们考虑可压缩Navier-Stokes系统与控制磁场时间演化的麦克斯韦方程组的耦合。引入相对熵泛函沿着耗散解的概念。作为应用的理论，我们表明，对于小的值的马赫数和大的雷诺数，全球在时间上弱（耗散）的解决方案收敛到理想的MHD系统描述的不可压缩的，无粘的，导电流体的运动。证明是基于无界域上的Neumann Laplacean的频率局部化Eschhartz估计。
We consider the compressible Navier-Stokes system coupled with the Maxwell equations governing the time evolution of the magnetic field. We introduce a relative entropy functional along with the related concept of dissipative solution. As an application of the theory, we show that for small values of the Mach number and large Reynolds number, the global in time weak (dissipative) solutions converge to the ideal MHD system describing the motion of an incompressible, inviscid, and electrically conducting fluid. The proof is based on frequency localized Strichartz estimates for the Neumann Laplacean on unbounded domains.