Navier-Stokes Existence and Smoothness: Analysis Through Temporal Dynamics Framework

This paper applies the Temporal Dynamics Framework to the Navier-Stokes existence and smoothness problem, one of the seven Clay Mathematics Institute Millennium Prize Problems. The problem asks whether smooth solutions to the Navier-Stokes equations in three dimensions always exist and remain smooth for all time. The analysis examines turbulence cascade structure, regularity analysis, and phi-to-pi decoherence interpretation of fluid dynamics singularities. This paper completes the Temporal Dynamics Framework coverage of all seven Clay Millennium Prize Problems. Paper 40 in the Temporal Dynamics Framework Research Series.