论文标题
关于弗拉索夫型方程的准化极限的最新发展
Recent developments on quasineutral limits for Vlasov-type equations
论文作者
论文摘要
Vlasov类型的动力学方程在血浆物理学中广泛用作模型。一个众所周知的例子是用于无碰撞，未磁化等离子体的Vlasov-Poisson系统。在这些注释中，我们讨论了在准界限极限上的最新进展，在该准中性极限中，血浆的debye长度倾向于为零，这是应用中广泛假设的近似值。从此极限中从弗拉索夫 - 波森系统正式获得的模型可以看作是Euler方程的动力学公式。但是，对此极限的严格结果通常需要结构性或强的规律性条件。在这里，我们介绍了Vlasov-Poisson系统的变体的最新结果，该变体在无质量电子方面对离子进行建模。在具有粗糙初始数据的设置中，我们讨论了该系统从该系统到动力学等热欧拉系统的列中和限制。然后，我们考虑了准中性极限与从粒子系统得出这些模型的问题之间的联系。我们首先提出了最新的结果，该结果是从vlasov-poisson系统的推导下，该系统带有来自扩展电荷系统的无质量电子。最后，我们讨论了一个组合限制，其中动力学等温欧拉系统得出。
Kinetic equations of Vlasov type are in widespread use as models in plasma physics. A well known example is the Vlasov-Poisson system for collisionless, unmagnetised plasma. In these notes, we discuss recent progress on the quasineutral limit in which the Debye length of the plasma tends to zero, an approximation widely assumed in applications. The models formally obtained from Vlasov-Poisson systems in this limit can be seen as kinetic formulations of the Euler equations. However, rigorous results on this limit typically require a structural or strong regularity condition. Here we present recent results for a variant of the Vlasov-Poisson system, modelling ions in a regime of massless electrons. We discuss the quasineutral limit from this system to the kinetic isothermal Euler system, in a setting with rough initial data. Then, we consider the connection between the quasineutral limit and the problem of deriving these models from particle systems. We begin by presenting a recent result on the derivation of the Vlasov-Poisson system with massless electrons from a system of extended charges. Finally, we discuss a combined limit in which the kinetic isothermal Euler system is derived.
