Abstract
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.
Original language | English (US) |
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Article number | 244002 |
Journal | Physical Review Letters |
Volume | 130 |
Issue number | 24 |
DOIs | |
State | Published - Jun 16 2023 |
ASJC Scopus subject areas
- General Physics and Astronomy