The Energy Based Near Singularity for Fourier Spectral 3D Navier-Stokes Equations
Numerical Analysis
2026-05-19 v2 Numerical Analysis
Abstract
We investigate the three-dimensional incompressible Navier-Stokes equations. The equations are discretized with Fourier spectral method and a fourth-order Runge-Kutta scheme in time. The spectral accuracy, resolution conditions, and an energy based conditional regularity framework are established analytically. Then we prove exponential convergence, algebraic convergence, and an a posteriori criterion that links numerical blowup to loss of regularity. This work develops a suite of diagnostics for detecting potential finite time singular behavior.
Keywords
Cite
@article{arxiv.2604.23159,
title = {The Energy Based Near Singularity for Fourier Spectral 3D Navier-Stokes Equations},
author = {Beibei Li},
journal= {arXiv preprint arXiv:2604.23159},
year = {2026}
}