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Abstract In this paper, we consider the long wavelength limit for the Euler-Poisson system arising in plasma including three species. It is demonstrated that when the plasma has critical densities,… Click to show full abstract
Abstract In this paper, we consider the long wavelength limit for the Euler-Poisson system arising in plasma including three species. It is demonstrated that when the plasma has critical densities, the modified Korteweg-de Vries (mKdV) equation can be derived, under the classical Gardner-Morikawa transform e 1 / 2 ( x − V t ) → x , e 3 / 2 t → t as e → 0 , with the velocity V depending on the densities. We estimate the error between the mKdV equation and the Euler-Poisson system in Sobolev spaces. The mKdV dynamics can be seen at time interval of order O ( e − 1 ) .
Journal Title: Journal of Differential Equations
Year Published: 2021
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