Navier–Stokes · visual study
The geometry of a
possible singularity.
Five visual steps connect fluid motion to the precise estimate that remains open. Begin with the arrows; the proof graph comes last.
Conceptual model · not a numerical simulationArrow direction is the axis of rotation. Arrow length is its strength.
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Start with tiny spinning arrows.
The velocity field says where the fluid moves. Its curl, called vorticity, says how the fluid spins. Each point gets an arrow: direction records the spin axis; length records intensity.
ω = ∇ × umotion → local rotation
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A long arrow does not mean the fluid travels in that direction. It means the local rotation around that axis is strong.