OpenAI construction · 8 September 2026
A vortex that runs to infinity.
The 3-D incompressible Navier–Stokes equations can start from rest, stay at finite energy, and still develop unbounded speed in finite time — driven only by a smooth force. The solution is a spinning swirl that spirals inward and stretches like spaghetti.
- Statement
- C and D
- Speed
- τ⁻½⁻ʰ
- Energy
- bounded
- Viscosity
- any ν > 0
This exhibit integrates the constructed self-similar field in three dimensions: Burgers swirl, axial stretching, and the published scaling with h = 0.005. Tracers follow the flow; the core shrinks while material filaments elongate.
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