On the Singular Geometric Discontinuity of the Compressible Navier-Stokes Equations Under Extreme External Forcing: A Density-Diffusion Limit Analysi

This paper presents a reformative approach to the 3D compressible Navier-Stokes equa-tions under extreme external forcing. By systematically eliminating macroscopic pressure and dy-namic viscosity representations via microscopic kinetic-theory transformations, the governing equa-tions are reduced entirely to density (ρ) and velocity (u) fields. Under high-velocity limits wherethe bulk velocity exceeds the characteristic molecular diffusion velocity (U ≫ C), we analyticallydemonstrate that the spatial density gradient undergoes a singular contraction (dρ → 0), inducinga structural breakdown in the continuum manifold. Integrating adiabatic thermal-energy transfor-mations, we prove that as velocity approaches infinity under external forcing, the system encountersa sharp geometric discontinuity characterized by a thermal collapse to absolute zero. This frame-work provides an explicit analytical representation of finite-time shock singularity without relyingon empirical non-Newtonian parameterizations.