SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 3040-3071, January 2021.
We study the global wellposedness of pressureless Eulerian dynamics in multidimensions, with radially symmetric data. Compared with the one-dimensional system, a major difference in multidimensional Eulerian dynamics is the presence of the spectral gap, which is difficult to control in general. We propose a new pair of scalar quantities that provides significantly better control of the spectral gap. Two applications are presented: (i) the Euler--Poisson equations: we show a sharp threshold condition on initial data that distinguish global regularity and finite time blowup; (ii) the Euler-alignment equations: we show a large subcritical region of initial data that leads to global smooth solutions.

中文翻译：

---

径向对称的多维欧拉动力学

SIAM数学分析杂志，第53卷，第3期，第3040-3071页，2021年1月。
我们使用径向对称数据研究了多维无压欧拉动力学的整体适度性。与一维系统相比，多维欧拉动力学的主要区别在于光谱间隙的存在，这通常很难控制。我们提出了一对新的标量，可以显着更好地控制光谱间隙。提出了两个应用：（i）欧拉-泊松方程：我们在初始数据上显示了一个尖锐的阈值条件，该条件可以区分全局规律性和有限时间膨胀；（ii）欧拉对准方程：我们显示了一个大的亚临界初始数据区域，可导致整体光滑解。