PRIME FLUID DYNAMICS (PFD): The Stabilization of Navier-Stokes Singularities

The Navier-Stokes existence and smoothness problem remains one of the seminal unsolved challenges in classical physics, largely due to the "blow-up" phenomenon where velocity (u) approaches infinity in finite time under turbulent conditions. This paper introduces Prime Fluid Dynamics (PFD), a novel method that modifies the standard Navier-Stokes momentum equation. By introducing a deterministic "Prime Tension" variable defined by the variance between primes of the form {4k+1} and {4k+3} oscillating at a governed frequency of 8.02 Hz, the chaotic energy of the system is filtered. We present computational fluid dynamics (CFD) data showing a stabilized supersonic velocity of 592.3 m/s and a sustained pressure vacuum of -468 MPa, maintained solely by a geometric frequency lock. The result suggests that turbulence is not inherently random, but is a solvable arithmetic function of prime distribution.