Subsonic Flow for the Multidimensional Euler-Poisson System

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We establish the existence and stability of subsonic potential flow for the steady Euler-Poisson system in a multidimensional nozzle of a finite length when prescribing the electric potential difference on a non-insulated boundary from a fixed point at the exit, and prescribing the pressure at the exit of the nozzle. The Euler-Poisson system for subsonic potential flow can be reduced to a nonlinear elliptic system of second order. In this paper, we develop a technique to achieve a priori estimates of solutions to a quasi-linear second order elliptic system with mixed boundary conditions in a multidimensional domain enclosed by a Lipschitz continuous boundary. In particular, we discovered a special structure of the Euler-Poisson system which enables us to obtain estimates of the velocity potential and the electric potential functions, and this leads us to establish structural stability of subsonic flows for the Euler-Poisson system under perturbations of various data.
Publisher
SPRINGER
Issue Date
2016-04
Language
English
Article Type
Article
Citation

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, v.220, no.1, pp.155 - 191

ISSN
0003-9527
DOI
10.1007/s00205-015-0930-6
URI
http://hdl.handle.net/10203/280616
Appears in Collection
MA-Journal Papers(저널논문)
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