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

RenJun Duan; ShuangQian Liu; HaiYan Yin; ChangJiang Zhu

doi:10.1007/s11425-015-5059-4

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

RenJun Duan, ShuangQian Liu, HaiYan Yin, ChangJiang Zhu^*

^*Corresponding author for this work

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

27 Citations (Scopus)

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.

Original language	English
Pages (from-to)	67-84
Journal	Science China Mathematics
Volume	59
Issue number	1
DOIs	https://doi.org/10.1007/s11425-015-5059-4
Publication status	Published - 1 Jan 2016
Externally published	Yes

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Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

Research Keywords

rarefaction wave
stability
two-fluid plasma model

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title = "Stability of the rarefaction wave for a two-fluid plasma model with diffusion",

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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AU - Duan, RenJun

AU - Liu, ShuangQian

AU - Yin, HaiYan

AU - Zhu, ChangJiang

N1 - Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

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N2 - 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.

AB - 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.

KW - rarefaction wave

KW - stability

KW - two-fluid plasma model

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EP - 84

JO - Science China Mathematics

JF - Science China Mathematics

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

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