Abstract We investigate the quasi-neutral limit (the zero Debye length limit) for the Euler-Poisson system with radial symmetry in an annular domain. Under physically relevant conditions at the boundary, referred to as the Bohm criterion, we first construct the approximate solutions by the method of asymptotic expansion in the limit parameter, the square of the rescaled Debye length, whose detailed derivation and analysis are carried out in our companion paper [8] . By establishing H m -norm, ( m ≥ 2 ) , estimate of the difference between the original and approximation solutions, provided that the well-prepared initial data is given, we show that the local-in-time solution exists in the time interval, uniform in the quasi-neutral limit, and we prove the difference converges to zero with a certain convergence rate validating the formal expansion order. Our results mathematically justify the quasi-neutrality of a plasma in the regime of plasma sheath, indicating that a plasma is electrically neutral in bulk, whereas the neutrality may break down in a scale of the Debye length.

中文翻译：

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环形域中存在边界层时 Euler-Poisson 系统的准中性极限

摘要 我们研究了在环形域中具有径向对称性的 Euler-Poisson 系统的准中性极限（零德拜长度极限）。在边界处的物理相关条件下，称为 Bohm 准则，我们首先通过极限参数渐近展开的方法构造近似解，重新缩放的德拜长度的平方，其详细推导和分析在我们的配套论文 [8] 。通过建立 H m -norm, ( m ≥ 2 ) ，估计原始解与近似解之间的差异，假设给定了精心准备的初始数据，我们证明局部时间解存在于时间间隔中, 在准中性极限均匀, 并且我们证明了差异收敛到零并具有一定的收敛速度，从而验证了正式的扩展顺序。我们的结果在数学上证明了等离子体鞘区中等离子体的准中性，表明等离子体在整体上是电中性的，而中性可能会在德拜长度的范围内分解。