Reproduce “Finite Time Blowup for Navier–Stokes” on OpenResearch
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About this paper
The paper constructs a smooth forced three-dimensional incompressible Navier–Stokes solution from rest whose speed becomes unbounded as t approaches 1 while kinetic energy remains uniformly bounded. A shrinking spinning vortex and oscillatory disturbances cancel the vortex’s annular momentum residual through averaged nonlinear flux; corrections make the force smooth and compactly supported. It concerns designed forcing, not unforced equations or arbitrary forces.
Key insights
- Singularity formation can be driven by a novel mechanism where small-scale, dynamically amplified oscillatory pulses generate a large-scale mean momentum flux.
- Maintaining a smooth, compactly supported external force for a blowup solution requires intricate cancellations of potentially unbounded terms in the momentum equation, achieved through precise multi-scale control.
- The construction effectively manages nonlinear interactions across numerous scales, ensuring that derivative bounds and incompressibility are maintained throughout the process.
Summary by alphaXiv.
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