Choose the flow.
Read its force.
Acceleration and viscous compensation share one signed scale. The third gauge adds them to reveal the force this flow needs.
Window: velocity ±2, upper trace · force ±36, lower trace. Probe velocity / force: . Time: .
Reduced motion is enabled. Choose still frames with the controls.
What this bench explains
On a2π-periodic3D domain, choose u=(0,A(t)sin(kx),0),p=0 and A(t)=a sin(ωt). Divergence and nonlinear transport are zero. The required force is f=(0,[A′+νk²A]sin(kx),0).
The gauges share ±36. Both traces span x0–2π, with different fixed vertical scales stated above. Dot coordinates and local readings follow the same exact field. Energy E=A²/4, input power P=f̂A/2 and dissipation D=νk²A²/2 give E′=P−D. Negative input power removes energy; dissipation stays nonnegative.
This flow starts at rest and stays bounded. Its force is analytic and periodic, not compactly supported or rapidly decaying in time. It is not a singularity example or a Clay C/D witness. No general3D regularity, blowup construction, Lean fidelity or episode research claim is verified here.
Fefferman: equations and force assumptions ↗
OpenAI: residual-force motivation ↗