Problem dossier · Dynamics & Analysis
Regularity & blow-up in model fluid equations
Do smooth solutions of simplified fluid models (1D model equations, axisymmetric Euler scenarios, generalized SQG) blow up in finite time — and what does the blow-up profile look like?
§1
Status
Active frontier: Elgindi's singularity for C^{1,α} Euler and Hou-type numerics for axisymmetric blow-up mark the state of the art; smooth-data Euler blow-up remains open (and Navier–Stokes is a Millennium problem — out of scope here).
Think you can crack this one? Read the playbook before you announce →
§2
The Angle of Attack
High-resolution numerical experiments on model equations (De Gregorio, CKN-type scenarios); fit self-similar profiles and test stability of candidate blow-ups.
Tags: pde · euler · blow-up · numerics
§3
The Lab
No instruments built yet. When this problem gets tackled, its interactive instruments — explorers, searches, verifiers running in the browser — live here. See the Collatz dossier for what a fully tackled problem looks like.
§4
The Log
Empty. Work on this problem gets logged here as dated entries — constructions tried, code run, dead ends included. Dead ends are results.
§5
Related Problems
More open problems in Dynamics & Analysis and adjacent territory.
- Berry–Tabor conjecture — Dynamics & Analysis
- Birkhoff conjecture on integrable billiards — Dynamics & Analysis
- Outer billiards unboundedness — Dynamics & Analysis
- Sendov's conjecture — Dynamics & Analysis