DISCRETE REGULARITY MODEL FOR THE NAVIER-STOKES EQUATIONS IN THE TRUE REFOUNDATION

The Navier-Stokes equations describe the motion of fluids. Their continuous mathematical study encounters the possibility of singularities, where the velocity or its gradient becomes infinite in finite time. The TRUE framework, under refoundation, proposes to replace the infinitely divisible continuum with a discrete lattice of minimal step h zero. This document explores a discrete model of the Navier-Stokes equations. The derivatives are replaced by finite differences. The K field is defined as a local density of crispation. The local saturation threshold is the value one. The propagation threshold depends on the local structure. The discrete model avoids by construction the formation of singularities. The discrete solution remains bounded and regular. However, this result does not constitute a resolution of the Millennium Problem posed by the Clay Institute. The question of the convergence of the discrete solution to the classical continuous solution remains open