Abstract
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.
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Communicated by P. Rabinowitz
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Bae, M., Duan, B. & Xie, C. Subsonic Flow for the Multidimensional Euler–Poisson System. Arch Rational Mech Anal 220, 155–191 (2016). https://doi.org/10.1007/s00205-015-0930-6
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DOI: https://doi.org/10.1007/s00205-015-0930-6