Quasineutral Limit of Euler–Poisson System with and without Viscosity
Quasineutral Limit of Euler–Poisson System with and without Viscosity
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DOI：
10.1081/pde-120030403
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发表时间：
2005-01
影响因子：
1.9
通讯作者：
Shu Wang
中科院分区：
文献类型：
--
作者：
Shu Wang
摘要 研究了等离子体物理中具有和不具有粘性的欧拉-泊松系统环面𝕋 d , d ≥ 1 的准中性极限。准中性体系是不可压缩的欧拉或纳维-斯托克斯方程已被证明。同时，如果不可压缩的欧拉或纳维-斯托克斯方程的光滑解对于附近的初始数据全局存在，则也可以得到欧拉-泊松系统在环面𝕋 d ，d ≥ 1 中的大振幅光滑解的长期存在性，无论德拜长度 λ → 0 是否具有粘性。特别是，在任意时间间隔上都可以得到欧拉-泊松系统在环面 𝕋2 中具有或不具有粘性且具有足够小的德拜长度的大振幅光滑解的存在性。这些结果的证明基于经典能量方法、调制能量方法、迭代技术和标准紧致性论证的直接扩展。
Abstract The quasineutral limit of Euler–Poisson system with and without viscosity in plasma physics in the torus 𝕋 d , d ≥ 1 is studied. That quasineutral regimes are the incompressible Euler or Navier–Stokes equations is proven. In the mean time, long-time existence for large amplitude smooth solutions of Euler–Poisson system in torus 𝕋 d , d ≥ 1, with or without viscosity as the Debye length λ → 0 is also obtained provided that the smooth solution of incompressible Euler or Navier–Stokes equations exists globally for nearby initial data. In particular, the existence of large amplitude smooth solutions of Euler–Poisson system in torus 𝕋2 with or without viscosity and with sufficiently small Debye length is obtained on any arbitrary time interval. The proof of these results is based on a straightforward extension of the classical energy method, the modulated energy method, the iteration techniques and the standard compactness argument.