Uniformly Global Smooth Solutions and Convergence of Euler-Poisson Systems with Small Parameters
Uniformly Global Smooth Solutions and Convergence of Euler-Poisson Systems with Small Parameters
复制标题
DOI：
10.1137/140983276
复制
发表时间：
2015-04
期刊：
影响因子：
--
通讯作者：
Yue-Jun Peng
中科院分区：
文献类型：
--
作者：
Yue-Jun Peng
我们考虑在非磁化等离子体和半导体的建模中出现的具有小参数的欧拉—泊松系统。对于接近常平衡状态的初始数据，证明了关于参数的光滑解的一致全局存在性。这个结果使我们能够展示当每个参数趋于零时欧拉-泊松系统的全局实时收敛性。该证明基于统一的能量估计，对所有参数都有效。用参数的形式给出了初始数据的小条件。
We consider an Euler--Poisson system with small parameters arising in the modeling of unmagnetized plasmas and semiconductors. For initial data close to constant equilibrium states, we prove the uniformly global existence of smooth solutions with respect to the parameters. This result allows us to show the global-in-time convergence of the Euler--Poisson system as each of the parameters goes to zero. The proof is based on unified energy estimates which are valid for all the parameters. The smallness conditions on the initial data are given explicitly in terms of the parameters.