论文标题
在2D Euler-Poisson方程的Riccati动力学上具有吸引力的强迫
On the Riccati dynamics of 2D Euler-Poisson equations 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，研究了一个控制二维EP方程的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，而其他涡度则进一步扩大了流动的爆炸行为。这些爆炸的扩增术语的增长与缺乏统一结合的Riesz的变换有关，因此很难研究多维EP系统的全球解决方案。我们表明，只要Riccati系统有能力拥有全球解决方案，只要增大术语的增长速度不高于指数，并且可以为大量初始配置提供全球平滑解决方案。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。还提出了一些数值示例。
The Euler-Poisson (EP) system describes the dynamic behavior of many important physical flows. In this work, a Riccati system that governs two-dimensional EP equations 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 further amplify the blow-up behavior of a flow. The growth of these blow-up amplifying terms are related to the Riesz transform of density, which lacks a uniform bound makes it difficult to study global solutions of the multi-dimensional EP system. We show that the Riccati system can afford to have global solutions, as long as the growth rate of blow-up amplifying terms is not higher than exponential, 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. Some numerical examples are also presented.
