Archive for Rational Mechanics and Analysis

, Volume 220, Issue 1, pp 155–191 | Cite as

Subsonic Flow for the Multidimensional Euler–Poisson System



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 \({C^{1,\alpha}}\) 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 \({C^{1,\alpha}}\) 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.


Weak Solution Elliptic System Subsonic Flow Background Solution Euler System 
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© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of MathematicsPOSTECHPohangKorea
  2. 2.School of Mathematical SciencesDalian University of TechnologyDalianChina
  3. 3.School of Business Informatics and MathematicsUniversity of MannheimMannheimGermany
  4. 4.Department of Mathematics, Institute of Natural Sciences, Ministry of Education Key Laboratory of Scientific and Engineering Computing, SHL-MACShanghai Jiao Tong UniversityShanghaiChina

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