研究
星期六, 31 7月 2021 09:02

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

 

Eitan Tadmor, and Changhui Tan

SIAM Journal on Mathematical Analysis, Volume 54, No. 4, pp. 4277-4296 (2022)


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.


   doi:10.1137/21M1437767
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 This work is supported by NSF grant DMS #1853001 and DMS #2108264
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