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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Qufu Normal University, Qufu, 273165, Shandong, China

    Cunming Liu

  2. Department of Mathematics, Taiyuan University of Technology, Taiyuan, 030024, China

    Cunming Liu

  3. Université Clermont Auvergne, CNRS, Laboratoire de Mathématiques Blaise Pascal, 63000, Clermont-Ferrand, France

    Yue-Jun Peng

Authors
  1. Cunming Liu
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  2. Yue-Jun Peng
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Correspondence to Yue-Jun Peng.

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Liu, C., Peng, YJ. Stability of periodic steady-state solutions to a non-isentropic Euler–Maxwell system. Z. Angew. Math. Phys. 68, 105 (2017). https://doi.org/10.1007/s00033-017-0848-y

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  • DOI: https://doi.org/10.1007/s00033-017-0848-y

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