双流体 Euler-Poisson 方程的长波长极限

Abstract

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

Li Min, Pu Xueke. Long-Wavelength Limit for the Two-Fluid Euler-Poisson Equation[J].Acta mathematica scientia,Series A, 2023, 43(2): 399-420.

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References 18

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

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