论文标题
径向对称性多维中的欧拉动力学
Eulerian dynamics in multi-dimensions with radial symmetry
论文作者
论文摘要
我们研究了具有径向对称数据的多维中无压力欧拉动力学的全球良好性。与1D系统相比，多维欧拉动力学的主要差异是光谱间隙的存在，这通常很难控制。我们提出了一对新的标量量，可以更好地更好地控制光谱差距。提出了两个申请。 （i）Euler-Poisson方程：我们在区分全球规律性和有限时间爆炸的初始数据上显示出急剧的阈值条件； （ii）Euler-Alignment方程：我们显示了导致全局平滑解决方案的初始数据的一个较大的亚临界区域。
We study the global wellposedness of pressure-less Eulerian dynamics in multi-dimensions, with radially symmetric data. Compared with the 1D system, a major difference in multi-dimensional 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 a significant 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.
