双流体Euler-Poisson方程的长波长极限

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

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.