“Breaking Through the Navier–Stokes Millennium Problem via Experiments and Equations”

This dataset presents experimental and mathematical results that aim to break through the long-standing Navier–Stokes Millennium Problem. By conducting controlled vortex flow experiments and applying AI-based video analysis, new equations have been derived under the Suction-Induced Inflow Extension Model (SIIEM). These equations describe the mechanisms of vortex core formation and collapse, offering a quantitative pathway that overcomes the limitations of classical Navier–Stokes analysis. The dataset includes short notes written in lemma–theorem–proof style, experimental records, and equation summaries. Together, these materials provide both a physical and mathematical foundation for interpreting regularity and smoothness in three-dimensional fluid flows, suggesting a new direction toward resolving one of the most fundamental open problems in mathematics and physics.