Critical threshold for global regularity of Euler-Monge-Amp\`ere system with radial symmetry
Analysis of PDEs
2021-12-23 v2 Mathematical Physics
math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.2108.00120,
title = {Critical threshold for global regularity of Euler-Monge-Amp\`ere system with radial symmetry},
author = {Eitan Tadmor and Changhui Tan},
journal= {arXiv preprint arXiv:2108.00120},
year = {2021}
}