Global Regularity of Band-Limited Navier–Stokes Equations

This preprint establishes global existence and regularity for the three-dimensional incompressible Navier–Stokes equations under a fixed spectral cutoff. By restricting the nonlinear interaction to a bounded Fourier band, we show that enstrophy remains uniformly bounded in time via a Bernstein inequality. As a result, finite-time singularities are excluded within this admissible class of band-limited flows. The work provides a mathematically consistent effective model illustrating how spectral constraints prevent blow-up, without addressing the unrestricted continuum problem.