3 years ago

Convergence of a non-isentropic Euler–Poisson system for all time

Cunming Liu, Yue-jun Peng

Publication date: November 2018

Source: Journal de Mathématiques Pures et Appliquées, Volume 119

Author(s): Cunming Liu, Yue-Jun Peng

Abstract

We consider periodic smooth solutions for a non-isentropic Euler–Poisson system with small parameters, in which the momentum and energy equations are partially dissipative. When initial data are close to constant equilibrium states, we prove the global-in-time convergence of the system as parameters go to zero. The limit systems are incompressible Euler equations with dissipation, the drift-diffusion system and the energy-transport system. The proof of the results is based on compactness arguments and uniform energy estimates with respect to the time and the parameters.

Résumé

Nous considérons les solutions régulières périodiques pour un système d'Euler–Poisson non isentropique avec petits paramètres, dans lequel les équations de la quantité de mouvement et de l'énergie sont dissipatives. Pour des données initiales proches d'états d'équilibre constants, nous démontrons la convergence globale en temps du système quand des paramètres tendent vers zéro. Les systèmes de limites sont les équations d'Euler incompressibles avec dissipation, le système de dérive-diffusion et le système de transport d'énergie. La démonstration des résultats repose sur des arguments de compacité et des estimations d'énergie uniformes par rapport au temps et aux paramètres.

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