Chronoflux Embedding and Intrinsic Regularisation of 3D Navier–Stokes

This paper studies the three-dimensional incompressible Navier–Stokes equation within an extended continuum framework in which a scalar regulator arises from a conserved temporal field. The Navier–Stokes equation appears as the acoustic limit of the temporal continuum, and the regulator is obtained from a local scalar closure consistent with covariance and positivity.

The resulting equation contains an intrinsic damping term that yields a Lyapunov inequality for the enstrophy. Under a lower bound on the regulator the inequality provides global control of the flow, preventing finite-time blow-up in the extended system. A covariant formulation is given, and the weak-field limit reproduces the damped acoustic Navier–Stokes equation.

Direct numerical simulation of the Taylor–Green vortex shows monotonic suppression of enstrophy as the regulator increases. The construction does not prove regularity of the classical Navier–Stokes equation, but defines a regularised system in which the damping term follows from a conservation law rather than from phenomenological forcing.

This work forms part of the Chronoflux research series on intrinsic continuum formulations of time and hydrodynamics.