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Global convergence of the Euler‐Poisson system for ion dynamics
Author(s) -
Liu Cunming,
Peng Yuejun
Publication year - 2018
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.5428
Subject(s) - convergence (economics) , euler equations , euler's formula , relaxation (psychology) , limit (mathematics) , boltzmann equation , mathematical analysis , compact space , constant (computer programming) , mathematics , diffusion , boltzmann constant , physics , statistical physics , quantum mechanics , computer science , psychology , social psychology , economics , programming language , economic growth
We consider smooth solutions of the Euler‐Poisson system for ion dynamics in which the electron density is replaced by a Boltzmann relation. The system arises in the modeling of plasmas, where appear two small parameters, the relaxation time and the Debye length. When the initial data are sufficiently close to constant equilibrium states, we prove the convergence of the system for all time, as each of the parameters goes to zero. The limit systems are drift‐diffusion equations and compressible Euler equations. The proof is based on uniform energy estimates and compactness arguments.