Gérard-Varet, David; Han-Kwan, Daniel; Rousset, Frédéric Quasineutral limit of the Euler-Poisson system for ions in a domain with boundaries. (English) Zbl 1417.35119 Indiana Univ. Math. J. 62, No. 2, 359-402 (2013). 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). Cited in 1 ReviewCited in 37 Documents 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 Keywords:isothermal Euler-Poisson; quasineutral limit; boundary layers; modulated linearized energy Citations:Zbl 0978.82086; Zbl 1417.35120 PDF BibTeX XML Cite \textit{D. Gérard-Varet} et al., Indiana Univ. Math. J. 62, No. 2, 359--402 (2013; Zbl 1417.35119) Full Text: DOI arXiv Link OpenURL