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\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 $ \mathbb{R}^3$, the validity of such an expansion is established even with ``ill-prepared'' Cauchy data, by including an additional initial layer correction.
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Derivation of the ion equation
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 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, the validity of such
an expansion is established even with \ill-prepared" Cauchy data, by including
an additional initial layer correction.
more »
« less
- Award ID(s):
- 1810868
- NSF-PAR ID:
- 10157527
- Date Published:
- Journal Name:
- Quarterly of applied mathematics
- Volume:
- 78
- Issue:
- 2
- ISSN:
- 0033-569X
- Page Range / eLocation ID:
- 305-332
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
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