Finite-Time Weak Singularities and the Statistical Structure of Turbulence in 3D Incompressible Navier-Stokes Equations
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910107104706560 |
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| author | Kit, Chio Chon |
| author_facet | Kit, Chio Chon |
| contents | This paper provides a rigorous mathematical analysis of the global regularity problem for the 3D incompressible Navier-Stokes (NS) equations, specifically addressing the conditions under which smooth initial data may lead to a loss of regularity. By departing from traditional phenomenological turbulence models and focusing strictly on the mechanical energy transport equation, we derive a fundamental critical condition, $\boldsymbol{u}\cdot\nabla E = 0,$ where $E = \frac12|\boldsymbol{u}|^2 + p$ is the specific mechanical energy, which characterizes the transition from laminar to turbulent flow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_28308 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Finite-Time Weak Singularities and the Statistical Structure of Turbulence in 3D Incompressible Navier-Stokes Equations Kit, Chio Chon Analysis of PDEs Fluid Dynamics This paper provides a rigorous mathematical analysis of the global regularity problem for the 3D incompressible Navier-Stokes (NS) equations, specifically addressing the conditions under which smooth initial data may lead to a loss of regularity. By departing from traditional phenomenological turbulence models and focusing strictly on the mechanical energy transport equation, we derive a fundamental critical condition, $\boldsymbol{u}\cdot\nabla E = 0,$ where $E = \frac12|\boldsymbol{u}|^2 + p$ is the specific mechanical energy, which characterizes the transition from laminar to turbulent flow. |
| title | Finite-Time Weak Singularities and the Statistical Structure of Turbulence in 3D Incompressible Navier-Stokes Equations |
| topic | Analysis of PDEs Fluid Dynamics |
| url | https://arxiv.org/abs/2603.28308 |