Project / Live interactive explainer
Navier-Stokes visual explainer
Follow a shrinking swirl through five interactive chapters to see how speed can rise while core energy falls.
- fluid-dynamics
- visualization
- mathematics
Follow the motion
A shrinking region of fluid can move faster while containing less energy. This explainer makes that idea visible, one step at a time.
Open the interactive explainer and follow the moving dots. Five chapters connect the shrinking swirl to the claim in OpenAI's paper, Finite Time Blowup for Navier-Stokes.
What to try
- Follow fluid as it spirals inward and leaves above or below.
- Move the slider to shrink the fast region.
- Compare rising speed with falling energy inside that region.
- Watch fine ripples grow and fade around the core.
- Open the source notes to connect the pictures to the equations.
What the pictures mean
The animation uses schematic paths and rescales the shapes so they stay visible. The numerical bars follow the paper's leading scaling laws near the claimed singularity. They measure changes relative to an earlier moment.
The model does not solve the fluid equations or verify the proof. The core energy bar covers only the shrinking region.
The paper's claim concerns the complete flow, with a carefully chosen external force. The explainer stops before the mathematical limit, so every displayed number stays finite.
Read the source paper for the construction and proof.