Convergence of compressible Euler–Poisson equations to incompressible type Euler equations

Article type: Research Article

Authors: Peng, Yue‐Jun^; | Wang, Ya‐Guang

Affiliations: Laboratoire de Mathématiques, CNRS UMR 6620, Université Blaise Pascal (Clermont‐Ferrand 2), 63177 Aubière cedex, France, E‐mail: [email protected]‐bpclermont.fr | Department of Mathematics, Shanghai Jiao Tong University, 200030 Shanghai, China E‐mail: [email protected]

Note: [] Corresponding author.

Abstract: In this paper, we study the convergence of time‐dependent Euler–Poisson equations to incompressible type Euler equations via the quasi‐neutral limit. The local existence of smooth solutions to the limit equations is proved by an iterative scheme. The method of asymptotic expansion and the symmetric hyperbolic property of the systems are used to justify the convergence of the limit.

Keywords: Euler–Poisson equations, incompressible Euler equations, quasi‐neutral limit, asymptotic expansion and justification

Journal: Asymptotic Analysis, vol. 41, no. 2, pp. 141-160, 2005