A Quantum-Corrected Navier–Stokes Framework via Madelung Hydrodynamics: From Quark-Gluon Plasma to Black Hole Singularity Resolution

This research presents a novel theoretical framework by integrating the Madelung hydrodynamics with the Navier–Stokes equations to address fundamental challenges in high-energy physics. We derive a "Quantum-Corrected Navier–Stokes" model that describes the dynamics of the Quark-Gluon Plasma (QGP) and provides a deterministic resolution to gravitational singularities within black holes. By introducing a viscosity-dependent quantum potential, the model eliminates stochastic behavior and classical singularities, suggesting a fluid-dynamic basis for spacetime evolution. This is part 1 of an ongoing research series. It establishes the mathematical foundation for fluid-quantum duality. part 2, which focuses on the nature of Dark Energy as a superfluid dynamic pressure and the deterministic cycle of the universe (The Big Crunch), is currently in development and will build directly upon these results.