标题： 欧拉-蒙日-阿普斯泰系统在径向对称下的全局正则性临界阈值 显示英文标题

标题： Critical threshold for global regularity of Euler-Monge-Ampère system with radial symmetry

摘要： 我们研究欧拉-蒙日-阿普斯托尔（EMA）系统的全局适定性。 我们在初始配置空间中获得了一个尖锐的、显式的临界阈值，该阈值保证了具有径向对称初始数据的EMA系统的全局正则性。 该结果是通过两种独立的方法获得的——一种是利用Liu & Tadmor [Comm. Math. Physics 228(3):435-466, 2002] 的谱动力学方法，另一种是基于Brenier & Loeper [Geom. Funct. Analysis 14(6):1182--1218, 2004] 的几何方法。 这些结果被扩展到带有旋涡的二维径向EMA系统。 显示英文摘要

摘要： We study the global wellposedness of the Euler-Monge-Amp\`ere (EMA) system. We obtain a sharp, explicit critical threshold in the space of initial configurations which guarantees the global regularity of EMA system with radially symmetric initial data. The result is obtained using two independent approaches -- one using spectral dynamics of Liu & Tadmor [Comm. Math. Physics 228(3):435-466, 2002] and another based on the geometric approach of Brenier & Loeper [Geom. Funct. Analysis 14(6):1182--1218, 2004]. The results are extended to 2D radial EMA with swirl.