Singularities of the Navier-Stokes and Euler equations
This text mentions work from 2024 on. Those parts were partly written without a live literature search and have not been checked by an editor yet.
The equations of fluid flow predict how velocity changes in time, and it is not known whether a smooth 3D flow always stays smooth or can develop infinite velocity in finite time (blowup). Since September 2026 several computer-generated blowup constructions have been claimed and are under examination.
Why it matters
Whether the basic equations of fluid motion can break down decides whether they are a complete description of fluids.
Review
J. Chen, T. Y. Hou, Stable nearly self-similar blowup of the 2D Boussinesq and 3D Euler equations with smooth data I: Analysis, arXiv, 2022. https://arxiv.org/abs/2210.07191 reference checked
Timestamp record
- Signed record
- 56471002f5ad…
- Public log
- Entry 258, in checkpoint 2,123
- In the log by
- Block 969,698, 2026-10-03
This text was in the PubPhys log by that date. The date says nothing about when the problem was first posed.