Quasi‑Trapping and Conditional Regularity for the 3D Navier–Stokes Equations

This paper introduces the notion of quasi‑trapping for the three‑dimensional Navier–Stokes equations and proves a conditional global regularity theorem. As stated in the abstract, “a subspace of the Fourier phase space is quasi‑trapping if the nonlinear term generates only a small fraction of energy outside it, relative to the energy inside,” and “if the initial data belong to a finite‑dimensional quasi‑trapping subspace, then the solution exists globally and is unique.” Numerical tests show that the low‑wavenumber subspace ∣k∣≤K is quasi‑trapping with an outside/inside ratio of approximately 2.5, providing a concrete numerical pathway toward resolving the Navier–Stokes regularity problem.