论文标题
二维欧拉 - 波森系统的全球解决方案具有吸引力的强迫
Global solutions for the two dimensional Euler-Poisson system with attractive forcing
论文作者
论文摘要
Euler-Poisson（EP）系统描述了许多重要的物理流动的动态行为。在这项工作中，研究了一个控制流量梯度的Riccati系统。差异的演变由带有几种非线性/非局部项的Riccati类型方程式控制。其中，涡度加速了差异，而其他涡度则抑制了差异并增强了流动的有限时间爆破。后一种术语的增长与这些术语的密度和非本地性的Riesz变换有关，因此很难研究多维EP系统的全球解决方案。尽管如此，我们表明Riccati系统可以负担得起在适当条件下的全球解决方案，并承认用于大量初始配置的全球平滑解决方案。为了证明这一点，我们在3D空间中构造了一个辅助系统，并找到系统的不变空间，然后与原始2D系统进行比较。本工作概括了几个以前的所谓限制/修改的EP模型。
The Euler-Poisson(EP) system describes the dynamic behavior of many important physical flows. In this work, a Riccati system that governs the flow's gradient is studied. The evolution of divergence is governed by the Riccati type equation with several nonlinear/nonlocal terms. Among these, the vorticity accelerates divergence while others suppress divergence and enhance the finite time blow-up of a flow. The growth of the latter terms are related to the Riesz transform of density and non-locality of these terms make it difficult to study global solutions of the multi-dimensional EP system. Despite of these, we show that the Riccati system can afford to have global solutions under a suitable condition, and admits global smooth solutions for a large set of initial configurations. To show this, we construct an auxiliary system in 3D space and find an invariant space of the system, then comparison with the original 2D system is performed. The present work generalizes several previous so-called restricted/modified EP models.
