The Energy Based Near Singularity for Fourier Spectral 3D Navier-Stokes Equations
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866909048200232960 |
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| author | Li, Beibei |
| author_facet | Li, Beibei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_23159 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Energy Based Near Singularity for Fourier Spectral 3D Navier-Stokes Equations Li, Beibei Numerical Analysis 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. |
| title | The Energy Based Near Singularity for Fourier Spectral 3D Navier-Stokes Equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2604.23159 |