Details

Autor(en) / Beteiligte

• Wang, Y
• Lai, C-Y
• Gómez-Serrano, J
• Buckmaster, T

Titel

Asymptotic Self-Similar Blow-Up Profile for Three-Dimensional Axisymmetric Euler Equations Using Neural Networks

Ist Teil von

• Physical review letters, 2023-06, Vol.130 (24), p.244002-244002, Article 244002

Ort / Verlag

United States

Erscheinungsjahr

2023

Quelle

EZB Electronic Journals Library

Beschreibungen/Notizen

• Whether there exist finite-time blow-up solutions for the 2D Boussinesq and the 3D Euler equations are of fundamental importance to the field of fluid mechanics. We develop a new numerical framework, employing physics-informed neural networks, that discover, for the first time, a smooth self-similar blow-up profile for both equations. The solution itself could form the basis of a future computer-assisted proof of blow-up for both equations. In addition, we demonstrate physics-informed neural networks could be successfully applied to find unstable self-similar solutions to fluid equations by constructing the first example of an unstable self-similar solution to the Córdoba-Córdoba-Fontelos equation. We show that our numerical framework is both robust and adaptable to various other equations.