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Chio Chon Kit

Publications and source records attributed to Chio Chon Kit.

4 recordsLinked to original sources
arXiv2026

Finite-Time Weak Singularities and the Statistical Structure of Turbulence in 3D Incompressible Navier-Stokes Equations

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.

math.AP↗
arXiv2026

Transition Time for Weak Singularities of the Navier-Stokes Equations

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 $\left\lVert \boldsymbol{u} \right\rVert_{H_0^1(\Omega)}\to0$, a closed analytical form of the laminar-turbulent transition characteristic time is derived. The theoretical scaling $t_{\text{trans}}\sim\nu/U^2$ (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.

math.AP↗
arXiv2026

Weak Singularity of Navier-Stokes Equations Based on Energy Estimation in Sobolev Space

Based on Dou Huashu's energy gradient theory, this paper focuses on the weak singularity of the incompressible Navier-Stokes (NS) equations in steady, fully developed flows. When the gradient of total mechanical energy is perpendicular to the streamline (i.e., $ u_j \frac{\partial E}{\partial x_j} = 0 $), substituting this critical condition into the NS equations with no-slip boundary conditions leads to the viscous term $ \nu \to 0 $. To rigorously analyze the regularity of the solution, Sobolev space $ H_0^1(\Omega) $ is introduced for energy estimation. The results show that the velocity field loses $ H^1 $-regularity, and the NS equations degenerate into Euler equations, which admit discontinuous weak solutions. Thus, the position where the mechanical energy gradient is perpendicular to the streamline becomes a weak singularity of the NS equations.

physics.flu-dyn↗