Scholarly record
Research summary
Conditional on finite maximal lifespan of a smooth unforced periodic three-dimensional Navier–Stokes history, amplitude-normalized records yield a bounded nonzero suitable ancient core. On fixed compact physical–spectral queries, original velocity, unit-ball-gauged canonical pressure, localized Fourier observations, and signed nonlinear work recover their same-core counterparts. Strong proper-past gradient convergence yields exact viscous dissipation and local kinetic-energy equality; countably registered queries admit one strict refinement. The initial-to-ancient energy balance requires positive historical donor work at each fixed sufficiently large radius. These are necessary properties of hypothetical breakdown histories, without a blowup construction or global-regularity conclusion.
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Scientific context
This paper belongs to the Fluid Dynamics & Navier–Stokes research program.