4 papers · 1 filter
Resolving Sharp Gradients of Unstable Singularities to Machine Precision via Neural Networks
Yongji Wang, Tristan Léger, Ching-Yao Lai +1
Recent work introduced a robust computational framework combining embedded mathematical structures, advanced optimization, and neural network architecture, leading to the discovery…
Discovery of Unstable Singularities
Yongji Wang, Mehdi Bennani, James Martens +19
Whether singularities can form in fluids remains a foundational unanswered question in mathematics. This phenomenon occurs when solutions to governing equations, such as the 3D Eul…
Smooth imploding solutions for 3D compressible fluids
Tristan Buckmaster, Gonzalo Cao-Labora, Javier Gómez-Serrano
Building upon the pioneering work [Merle, Raphaël, Rodnianski, and Szeftel, Ann. of Math., 196(2):567-778, 2022, Ann. of Math., 196(2):779-889, 2022, Invent. Math., 227(1):247-413…
Blowup for the defocusing septic complex-valued nonlinear wave equation in
Tristan Buckmaster, Jiajie Chen
In this paper, we prove blowup for the defocusing septic complex-valued nonlinear wave equation in . This work builds on the earlier results of Shao, Wei, and Zha…