  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.
