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The rigorous derivation of unipolar Euler–Maxwell system for electrons from bipolar Euler–Maxwell system by infinity‐ion‐mass limit
Author(s) -
Zhao Liang
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6950
Subject(s) - mathematics , euler's formula , limit (mathematics) , convergence (economics) , decoupling (probability) , electron , mathematical analysis , euler equations , maxwell's equations , infinity , physics , quantum mechanics , control engineering , engineering , economics , economic growth
In the paper, we consider the local‐in‐time and the global‐in‐time convergence of infinity‐ion‐mass limit for bipolar Euler–Maxwell systems by setting the mass of an electronm e = 1 and letting the mass of an ion m i → + ∞ . We use the method of asymptotic expansions to handle the local‐in‐time convergence problem and find that the limiting process from bipolar models to unipolar models is actually decoupling but not the vanishing of equations for the corresponding the other particle. Moreover, when the initial data are sufficiently close to the constant equilibrium state, we also establish the corresponding global‐in‐time convergence.