等离子体中双流体模型的调制逼近  

Modulation Approximation of a 2-Fluid System in Plasma

作　　者：刘慧敏 蒲学科 LIU Huimin;PU Xueke(School of Applied Mathematics,Shanxi University of Finance and Economics,Taiyuan 030006,P.R.China;School of Mathematics and Information Science,Guangzhou University,Guangzhou 510006,P.R.China)

机构地区：[1]山西财经大学应用数学学院,太原030006 [2]广州大学数学与信息科学学院,广州510006

出　　处：《应用数学和力学》2022年第9期944-954,共11页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(12001338,11871172);广东省自然科学基金(2019A1515012000);山西省高等学校科技创新项目(2020L0256)。

摘　　要：等离子体中的双流体模型描述了丰富的等离子体动力学行为,包括离子声波和等离子体波之间的相互作用.为了描述该双流体模型小振荡波包解包络的演化,利用多尺度分析方法将非线性Schrödinger(NLS)方程作为形式逼近方程导出,并通过对该双流体模型的真实解和逼近解之间的误差,在Sobolev空间中进行了一致能量估计,最终在时间尺度O(ε^(-2))上严格证明了NLS逼近的有效性.A kind of 2-fluid system in plasmas describes rich plasma dynamics,including the interactions between the ion acoustic wave and the plasma body wave.In order to describe the evolution of the envelope of the small oscillating wave packet solution of the 2-fluid model,the nonlinear Schrödinger(NLS)equation was derived as a formal approximation equation with the multi-scale analysis method,and the uniform energy estimation of the error between the exact solution and the approximate solution to the 2-fluid model was given in the Sobolev space.The NLS approximation was finally proved strictly on the time-scale O(ε^(-2)).

关 键 词：双流体模型 调制逼近 NLS方程 共振点 Normal-Form变换 

分 类 号：O175.2[理学—数学]