NLS approximation of the Euler-Poisson system for a cold ion-acoustic plasma
NLS approximation of the Euler-Poisson system for a cold ion-acoustic plasma
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DOI：
10.1016/j.jde.2023.09.035
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发表时间：
2024-01
影响因子：
2.4
通讯作者：
Huimin Liu;Dongfen Bian;Xueke Pu
中科院分区：
文献类型：
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作者：
Huimin Liu;Dongfen Bian;Xueke Pu
在之前的论文Liu和Pu（2019）[17]中，我们证明了热离子声等离子体的Euler-Poisson系统的非线性薛定谔（NLS）近似，其中共振的出现和二次项导数的损失是主要困难。注意，当离子-声等离子体是热的时，欧拉-泊松系统是弗里德里希可对称化的，并且线性项可以提供导数以补偿在对角化线性化系统之后由二次项引起的导数的损失。当离子声等离子体是冷的，如本文所考虑的，情况是非常不同的，在以前的文件。Euler-Poisson系统变成了无压系统，线性算子不再具有正则性，二次项在对角化系统中仍然损失一个导数。这一事实使得证明冷离子声等离子体中Euler-Poisson系统的NLS近似变得更加困难。本文利用无压Euler-Poisson系统的特殊结构和规范型变换，解决了共振引起的困难，特别是导数损失引起的困难，从而证明了NLS逼近。
In the previous paper Liu and Pu (2019) [17], we proved the nonlinear Schrödinger (NLS) approximation for the Euler-Poisson system for a hot ion-acoustic plasma, where the appearance of resonances and the loss of derivatives of quadratic terms are the main difficulties. Note that when the ion-acoustic plasma is hot, the Euler-Poisson system is Friedrich symmetrizable, and the linear term can provide a derivative to compensate the loss of derivative induced by quadratic terms after diagonalizing the linearized system. When the ion-acoustic plasma is cold, as considered in the present paper, the situation is very different from that in the previous paper. The Euler-Poisson system becomes a pressureless system, so the linear operator has no regularity, and the quadratic terms still lose a derivative in the diagonalized system. This fact makes it more difficult to prove the NLS approximation of Euler-Poisson system for a cold ion-acoustic plasma. In this paper, we take advantage of the special structure of the pressureless Euler-Poisson system and the normal-form transformation to deal with the difficulties caused by resonances, especially the difficulties caused by derivative loss, in order to prove the NLS approximation.