The long wavelength limit for the pressureless two-fluid Euler–Poisson system in three-dimensional whole space case is discussed in the present paper. It is shown that the smooth solutions for the two-fluid Euler–Poisson system converge strongly to those of the Zakharov–Kuznetsov equation in an $O\left({\epsilon }^{-3∕2}\right)$ time interval by the Gardner–Morikawa transform and the elaborate energy method.

中文翻译：

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无压两流体欧拉-泊松系统的色散极限

本文讨论了三维全空间情况下无压两流体Euler-Poisson系统的长波长限制。结果表明，二流体Euler-Poisson系统的光滑解与Zakharov-Kuznetsov方程的光滑解强烈收敛。$Ø（{\epsilon }^{-3∕2}）$ Gardner-Morikawa变换和精细的能量法确定时间间隔。