Levent Alpöge and Tristan Buckmaster announced a major breakthrough proving finite-time blowup with smooth forcing for the 3D incompressible Euler, Boussinesq, and inviscid primitive equations (IPM). This resolves long-standing open problems in mathematical fluid dynamics regarding whether smooth solutions to these fundamental equations can develop singularities in finite time.
Background
The question of whether smooth solutions to the 3D incompressible Euler equations can develop finite-time singularities is one of the most famous open problems in mathematical analysis, closely related to the Clay Mathematics Institute's Millennium Prize problems. The Boussinesq and inviscid primitive equations are closely related models used in geophysical fluid dynamics.
- Source
- Lobsters
- Published
- Sep 8, 2026 at 03:43 PM
- Score
- 9.0 / 10