Critical threshold for global regularity of Euler-Monge-Amp\`ere system with radial symmetry

Eitan Tadmor; Changhui Tan

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arXiv · 2108.00120

Critical threshold for global regularity of Euler-Monge-Amp\`ere system with radial symmetry

Eitan Tadmor·Changhui Tan

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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.

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Eitan Tadmor, Changhui Tan. 2021-07-31. Critical threshold for global regularity of Euler-Monge-Amp\`ere system with radial symmetry. https://arxiv.org/abs/2108.00120

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