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Saturday, 31 July 2021 09:02

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

 

Eitan Tadmor, and Changhui Tan


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.


 This work is supported by NSF grant DMS #1853001 and DMS #2108264

arXiv Preprint 2108.00120.

Read 194 times Last modified on Tuesday, 03 August 2021 10:02