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Stability of periodic steady-state solutions to a non-isentropic Euler–Maxwell system

  • Cunming Liu
  • Yue-Jun Peng
Article

Abstract

This paper is concerned with a stability problem in a periodic domain for a non-isentropic Euler–Maxwell system without temperature diffusion term. This system is used to describe the dynamics of electrons in magnetized plasmas when the ion density is a given smooth function which can be large. When the initial data are close to the steady states of the system, we show the global existence of smooth solutions which converge toward the steady states as the time tends to infinity. We make a change of unknown variables and choose a non-diagonal symmetrizer of the full Euler equations to get the dissipation estimates. We also adopt an induction argument on the order of derivatives of solutions in energy estimates to get the stability result.

Keywords

Euler–Maxwell system Global smooth solution Stability Steady-state solution Energy estimate 

Mathematics Subject Classification

35B40 35Q60 35Q35 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of MathematicsQufu Normal UniversityQufuChina
  2. 2.Department of MathematicsTaiyuan University of TechnologyTaiyuanChina
  3. 3.Université Clermont Auvergne, CNRS, Laboratoire de Mathématiques Blaise PascalClermont-FerrandFrance

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