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Quasineutral limit of the Euler-Poisson system for ions in a domain with boundaries. (English) Zbl 1417.35119

Summary: We study the quasineutral limit of the isothermal Euler-Poisson system describing a plasma made of ions and massless electrons. The analysis is achieved in a domain of \(\mathbb{R}^3\) and thus extends former results by S. Cordier and E. Grenier [Commun. Partial Differ. Equations 25, No. 5–6, 1099–1113 (2000; Zbl 0978.82086)], who dealt with the same problem in a one-dimensional domain without boundary.
For Part II, see J. Éc. Polytech., Math. 1, 343–386 (2014; Zbl 1417.35120).

MSC:

35Q35 PDEs in connection with fluid mechanics
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
81V35 Nuclear physics
35M33 Initial-boundary value problems for mixed-type systems of PDEs
78A48 Composite media; random media in optics and electromagnetic theory
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