Transition Time for Weak Singularities of the Navier-Stokes Equations
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915931298463744 |
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| author | Kit, Chio Chon |
| author_facet | Kit, Chio Chon |
| contents | This paper constructs a rigorous mathematical framework for investigating laminar-turbulent transition induced by weak singularities of incompressible Navier-Stokes (NS) equations. By integrating the energy identity of Leray weak solutions with the singularity criterion $\left\lVert \boldsymbol{u} \right\rVert_{H_0^1(Ω)}\to0$, a closed analytical form of the laminar-turbulent transition characteristic time is derived. The theoretical scaling $t_{\text{trans}}\simν/U^2$ (equivalent to $t_{\text{trans}}\sim t_c/\text{Re}$) is verified to be consistent with classical experimental observations in shear flows. This work reveals that laminar-turbulent transition is dominated by the local regularity collapse of Leray weak solutions rather than global viscous diffusion, and provides a novel theoretical interpretation for the onset of turbulence from the perspective of NS equation weak singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_09640 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Transition Time for Weak Singularities of the Navier-Stokes Equations Kit, Chio Chon Analysis of PDEs This paper constructs a rigorous mathematical framework for investigating laminar-turbulent transition induced by weak singularities of incompressible Navier-Stokes (NS) equations. By integrating the energy identity of Leray weak solutions with the singularity criterion $\left\lVert \boldsymbol{u} \right\rVert_{H_0^1(Ω)}\to0$, a closed analytical form of the laminar-turbulent transition characteristic time is derived. The theoretical scaling $t_{\text{trans}}\simν/U^2$ (equivalent to $t_{\text{trans}}\sim t_c/\text{Re}$) is verified to be consistent with classical experimental observations in shear flows. This work reveals that laminar-turbulent transition is dominated by the local regularity collapse of Leray weak solutions rather than global viscous diffusion, and provides a novel theoretical interpretation for the onset of turbulence from the perspective of NS equation weak singularities. |
| title | Transition Time for Weak Singularities of the Navier-Stokes Equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2604.09640 |