Acta mathematica scientia,Series A ›› 2023, Vol. 43 ›› Issue (2): 399-420.

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

Li Min1(),Pu Xueke2,*()   

  1. 1Faculty of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006
    2School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006
  • Received:2021-11-11 Revised:2022-09-13 Online:2023-04-26 Published:2023-04-17
  • Supported by:
    NSFC(11871172);NSFC(12201366);Science and Technology Projects in Guangzhou(202201020132);Applied Basic Research Program of Shanxi(20210302124380);Scientific and Technologial Innovation Programs of Higher Education Institutions in Shanxi(2020L0257)

Abstract:

In this paper, we justify rigorously the long-wavelength limit for the two-fluid Euler-Poisson matrix. Firstly, under a long wave scaling, we establish the formal derivation of the Korteweg-de Vries (KdV) matrix from the two-fluid Euler-Poisson matrix 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 matrix mathematically rigorously when $m_{i}/m_{e}\neq T_{i}/T_{e}$ in a time interval on which the KdV dynamics can be seen.

Key words: Two-fluid Euler-Poisson matrix, Long-wavelength limit, Singular perturbation method

CLC Number: 

  • O175.29
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