Global Solutions to the Isothermal Euler-Poisson System with Arbitrarily Large Data
Global Solutions to the Isothermal Euler-Poisson System with Arbitrarily Large Data
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DOI：
10.1006/jdeq.1995.1158
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发表时间：
1995-11
影响因子：
2.4
通讯作者：
F. Poupaud;M. Rascle;J. Vila
中科院分区：
文献类型：
--
作者：
F. Poupaud;M. Rascle;J. Vila
本文证明了一维几何中任意大数据情形下Euler-Poisson方程组解的整体存在性。我们所考虑的压强定律是从电子气的等温假设导出的。在这种情况下，Nishida已经指出，Glimm泛函的线性部分随着时间而减少。使用Glimm计划，他用这个属性来构建全球定义的弱解的欧拉系统任意大的数据。我们遵循他的证明大纲。在这里，由于电场的存在，源项出现了新的困难。关键的一点是Glimm格式几乎是保守的。这种电荷的准守恒导致对电场总变化的统一估计。这个估计允许证明该计划的收敛性。
Abstract We prove the global existence of a solution to the Euler-Poisson system, with arbitrarily large data, in a one-dimensional geometry. The pressure law we consider, is deduced from an isothermal assumption for the electrons gas. In this case, Nishida has already pointed out that the linear part of the Glimm functional is decreasing with respect to time. Using a Glimm scheme, he used this property to construct globally defined weak solutions for the Euler system with arbitrary large data. We follow his outline of proof. Here, a new difficulty arises with the source term, due to the electric field. A key point is that the Glimm scheme is almost conservative. This quasi-conservation of charge leads to a uniform estimate of the total variation of the electric field. This estimate allows to prove the convergence of the scheme.