双流体Euler-Poisson方程的长波长极限  

Long-Wavelength Limit for the Two-Fluid Euler-Poisson Equation

作　　者：李敏 蒲学科 Li Min;Pu Xueke(Faculty of Applied Mathematics,Shanxi University of Finance and Economics,Taiyuan 030006;School of Mathematics and Information Science,Guangzhou University,Guangzhou 510006)

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：《数学物理学报（A辑）》2023年第2期399-420,共22页Acta Mathematica Scientia

基　　金：国家自然科学基金(11871172,12201366);广州市科技计划项目(202201020132);山西省基础研究计划(20210302124380);山西省高等学校科技创新项目(2020L0257)。

摘　　要：该文研究双流体Euler-Poisson方程的长波长极限.首先,借助长波尺度变换和奇异摄动方法,建立了双流体Euler-Poisson方程到Korteweg-de Vries(KdV)方程的形式推导.然后,当m_(i)/m_(e)≠T_(i)/T_(e)时,通过深入分析余项方程的结构,并利用能量方法,从数学上严格证明此极限过程的合理性.其结果表明:在KdV方程解存在的时间范围内,双流体Euler-Poisson方程的解可收敛到KdV方程的解.In this paper,we justify rigorously the long-wavelength limit for the two-fluid Euler-Poisson equation.Firstly,under a long wave scaling,we establish the formal derivation of the Korteweg-de Vries(KdV)equation from the two-fluid Euler-Poisson equation by using a singular perturbation method.Then,with the aid of deep analysis of the complicated coupling structure of the two-fluid Euler-Poisson system and delicate energy estimates depending on such a structure,we prove the convergence of solutions of the Euler-Poisson system to that of the KdV equation mathematically rigorously when m_(i)/m_(e)≠T_(i)/T_(e)in a time interval on which the KdV dynamics can be seen.

关 键 词：双流体Euler-Poisson方程 长波长极限 奇异摄动方法 

分 类 号：O175.29[理学—数学]