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

2021/07/31 by Tadmor, Eitan, Tan, Changhui
#35B30 #35K96 #35Q35 #76N10 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2108.00120

Abstract

We study the global wellposedness of the Euler-Monge-Ampère (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.

Related

• Global Regularity of the 4D Restricted Euler Equations
• Eulerian dynamics in multi-dimensions with radial symmetry
• Critical thresholds in the Euler-Poisson-alignment system
• Global regularity of two-dimensional flocking hydrodynamics
• Global well-posedness and refined regularity criterion for the uni-directional Euler-alignment system