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Stability of the rarefaction wave for a two-fluid plasma model with diffusion

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Abstract

We study the large-time asymptotics of solutions toward the weak rarefaction wave of the quasineutral Euler system for a two-fluid plasma model in the presence of diffusions of velocity and temperature under small perturbations of initial data and also under an extra assumption

$\frac{{\theta _{i, + } }} {{\theta _{e, + } }} = \frac{{\theta _{i, - } }} {{\theta _{e, - } }} \geqslant \frac{{m_i }} {{2m_e }}, $

, namely, the ratio of the thermal speeds of ions and electrons at both far fields is not less than one half. Meanwhile, we obtain the global existence of solutions based on energy method.

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Authors and Affiliations

  1. Department of Mathematics, The Chinese University of Hong Kong, Hong Kong, 999077, China

    RenJun Duan

  2. Department of Mathematics, **an University, Guangzhou, 510632, China

    ShuangQian Liu

  3. School of Mathematical Sciences, Huaqiao University, Quanzhou, 362021, China

    HaiYan Yin

  4. School of Mathematics, South China University of Technology, Guangzhou, 510641, China

    ChangJiang Zhu

Authors
  1. RenJun Duan
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  2. ShuangQian Liu
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  3. HaiYan Yin
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  4. ChangJiang Zhu
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Correspondence to ChangJiang Zhu.

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Duan, R., Liu, S., Yin, H. et al. Stability of the rarefaction wave for a two-fluid plasma model with diffusion. Sci. China Math. 59, 67–84 (2016). https://doi.org/10.1007/s11425-015-5059-4

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  • DOI: https://doi.org/10.1007/s11425-015-5059-4

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