The global convergence of non-isentropic Euler–Maxwell equations via Infinity-Ion-Mass limit

Abstract

This paper is concerned with the periodic problem to the two-fluid non-isentropic Euler–Maxwell (N-E-M) equations. The equations arises in the modeling of magnetic plasma, in which appear two physical parameters, the mass of an electron \(m_\mathrm{e}\) and the mass of an ion \(m_{\mathrm{i}}\). With the help of methods of asymptotic expansions, we prove the local-in-time convergence of smooth solutions to this problem by setting \(m_\mathrm{e} = 1\) and letting \(m_{\mathrm{i}} \rightarrow +\infty \). Moreover, when the initial data are near constant equilibrium states, by means of uniform energy estimates and compactness arguments, we rigorously prove the infinity-ion-mass convergence of the system for all time. The limit system is the one-fluid N-E-M system.

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Acknowledgements

The authors are grateful to the referee for the comments. The first author would like to express his sincere gratitude to Professor Yue-Jun Peng of Université Clermont Auvergne for excellent directions in France. The authors are supported by the the BNSF (1164010, 1132006), NSFC (11771031, 11531010, 11831003), NSF of Qinghai Province (2017-ZJ-908), NSF of Henan Province (162300410084), the Key Research Fund of Henan Province (16A110019), the general project of scientific research project of the Beijing education committee of China(KM202111232008), the research fund of Beijing Information Science and Technology University (2025029).

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Correspondence to Xin Li.

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Feng, YH., Li, X. & Wang, S. The global convergence of non-isentropic Euler–Maxwell equations via Infinity-Ion-Mass limit. Z. Angew. Math. Phys. 72, 28 (2021). https://doi.org/10.1007/s00033-020-01459-6

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Keywords

  • Two fluids non-isentropic Euler–Maxwell equations
  • The infinity-ion-mass limit
  • Local convergence
  • Global convergence

Mathematics Subject Classification

  • 35Q35
  • 76N10