Tootfinder

Discovery of Unstable Singularities
Yongji Wang, Mehdi Bennani, James Martens, S\'ebastien Racani\`ere, Sam Blackwell, Alex Matthews, Stanislav Nikolov, Gonzalo Cao-Labora, Daniel S. Park, Martin Arjovsky, Daniel Worrall, Chongli Qin, Ferran Alet, Borislav Kozlovskii, Nenad Toma\v{s}ev, Alex Davies, Pushmeet Kohli, Tristan Buckmaster, Bogdan Georgiev, Javier G\'omez-Serrano, Ray Jiang, Ching-Yao Lai

Discovery of Unstable Singularities
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 Euler equations, develop infinite gradients from smooth initial conditions. Historically, numerical approaches have primarily identified stable singularities. However, these are not expected to exist for key open problems, such as the boundary-free Euler and Navier-Stokes cases, where unstable singularities are hypothesi…