Stability of periodic steady-state solutions to a non-isentropic Euler-Maxwell system
Stability of periodic steady-state solutions to a non-isentropic Euler-Maxwell system
复制标题
非等熵欧拉-麦克斯韦系统周期性稳态解的稳定性
DOI：
10.1007/s00033-017-0848-y
复制
发表时间：
2017
影响因子：
2
通讯作者：
Peng Yue Jun
中科院分区：
文献类型：
--
作者：
Liu Cunming;Peng Yue Jun
研究了一类不含温度扩散项的非等熵Euler-Maxwell系统在周期区域的稳定性问题。当离子密度是一个给定的光滑函数时，这个系统被用来描述磁化等离子体中电子的动力学。当初始值接近系统的稳态时，我们证明了光滑解的整体存在性，并且当时间趋于无穷大时，光滑解收敛到系统的稳态。我们对未知变量进行了改变，并选择了一个非对角对称化子的完整的欧拉方程得到的耗散估计。在能量估计中，我们还引入了解的导数阶的归纳论证，得到了稳定性结果。
This paper is concerned with a stability problem in a periodic domain for a non-isentropic Euler–Maxwell system without temperature diffusion term. This system is used to describe the dynamics of electrons in magnetized plasmas when the ion density is a given smooth function which can be large. When the initial data are close to the steady states of the system, we show the global existence of smooth solutions which converge toward the steady states as the time tends to infinity. We make a change of unknown variables and choose a non-diagonal symmetrizer of the full Euler equations to get the dissipation estimates. We also adopt an induction argument on the order of derivatives of solutions in energy estimates to get the stability result.