论文标题
双极欧拉 - 波森系统的无限 - 离子质量限制中的全局收敛和误差估计
Global Convergence and Error Estimates in Infinity-ion-mass Limits for Bipolar Euler-Poisson System
论文作者
论文摘要
本文涉及从双极欧拉 - 波森系统（BEP）到单极一（UEP）通过Infinity-ION-MAS质量极限的全球收敛，这是通过让离子$ M_I $的比率比Electron $ M_E $的质量的比率。对于足够接近恒定平衡状态的平滑溶液，获得了极限的整体收敛。此外，通过应用流函数方法并利用误差系统的反对称结构，可以在（BEP）和（UEP）平滑解决方案之间获得相应的全局误差估计。值得一提的是，由于双极系统中泊松方程的强耦合，因此应基于溶液的渐近扩展，与单极系统的情况非常不同，将离子和电子方程的流函数分别构建。
This paper is concerned with the global-in-time convergence from bipolar Euler-Poisson system (BEP) to unipolar one (UEP) through the infinity-ion-mass limit by letting the ratio of the mass of ion $m_i$ over that of electron $m_e$ goes to infinity. The global convergence of the limit is obtained for smooth solutions sufficiently close to constant equilibrium states. Furthermore, by applying the stream function method and taking advantage of the anti-symmetric structure of the error system, one obtains the corresponding global-in-time error estimates between smooth solutions of (BEP) and (UEP). It is worth mentioning that due to the strong coupling through the Poisson equation in bipolar system, stream functions for ions and electrons equations should be constructed separately based on asymptotic expansions of solutions, which is very different from the case of unipolar system.
