Derivation of the ion equation

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Abstract
We consider the classical Euler-Poisson system for electrons and ions, interacting through an electrostatic field. The mass ratio of an electron and an ion m e / M i ≪ 1 m_e/M_i\ll 1 is small and we establish an asymptotic expansion of solutions, where the main term is obtained from a solution to a self-consistent equation involving only the ion variables. Moreover, on R 3 \mathbb {R}^3 , the validity of such an expansion is established even with “ill-prepared” Cauchy data, by including an additional initial layer correction.
Funding Information
  • National Science Foundation (DMS-1700282)
  • Japan Society for the Promotion of Science (DMS-1700282)

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