dc.contributor.author
Wang, Y.
dc.contributor.author
Lai, C.-Y
dc.contributor.author
Gómez-Serrano, J.
dc.contributor.author
Buckmaster, T.
dc.date.accessioned
2023-08-28T13:30:00Z
dc.date.accessioned
2024-09-19T14:35:55Z
dc.date.available
2023-08-28T13:30:00Z
dc.date.available
2024-09-19T14:35:55Z
dc.date.issued
2023-06-16
dc.identifier.uri
http://hdl.handle.net/2072/536852
dc.description.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. © 2023 American Physical Society.
eng
dc.description.sponsorship
The authors were supported by the NSF Grants No. DMS-1900149 and No. DMS-1929284, ERC Grant No. 852741, the Spanish State Research Agency, through the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D (CEX2020-001084-M), Dean for Research Fund at Princeton University, the Schmidt DataX Fund at Princeton University, a Simons Foundation Mathematical and Physical Sciences Collaborative Grant, and grant from the Institute for Advanced Study. The simulations presented in this Letter were performed using the Princeton Research Computing resources at Princeton University and School of Natural Sciences Computing resources at the Institute for Advanced Study.
dc.format.extent
21 p.
cat
dc.publisher
American Physical Society
cat
dc.relation.ispartof
Physical Review Letters
cat
dc.source
RECERCAT (Dipòsit de la Recerca de Catalunya)
dc.subject.other
Fluid Dynamics, Deep learning, Machine learning, Navier-Stokes equation
cat
dc.title
Asymptotic Self-Similar Blow-Up Profile for Three-Dimensional Axisymmetric Euler Equations Using Neural Networks
cat
dc.type
info:eu-repo/semantics/article
cat
dc.type
info:eu-repo/semantics/submittedVersion
cat
dc.identifier.doi
10.1103/PhysRevLett.130.244002
cat
dc.rights.accessLevel
info:eu-repo/semantics/openAccess
