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Computer-assisted global regularity across nonlinear families of three-dimensional periodic Navier-Stokes flows

arXiv · AI, language, vision and robotics · article · Sep 14, 2026 · UTC

Numerical simulations reveal how vortices stretch and transfer energy, but establishing smooth evolution requires bounds that remain valid beyond the simulated resolution. Here I develop a computer-assisted framework that establishes global regularity for continuous families of three-dimensional periodic Navier-Stokes flows. Its central construction combines finite reference trajectories with a common error bound that covers an interval of centre fields and infinitely many smooth perturbation modes. The method retains the complete nonlinear residual before spectral truncation and controls the

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