Abstract
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(ε−3∕2) time interval by the Gardner–Morikawa transform and the elaborate energy method.
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