Revolution on Cardiac Fluid dynamic Systems: Correlating Navier--Stokes Finite-Time Singularities with cardiac fluid dynamics simulation and mathematical prediction

For nearly a century, the three-dimensional incompressible Navier--Stokes equations have served as the cornerstone of continuum fluid mechanics. Recent breakthroughs constructing finite-time singularities under smooth, compactly supported forcing have challenged classical assumptions about fluid regularity. After that the team of OpenAI found a “singularity” in the Navier-Stokes equations in three dimensions — thus resolving one of the six remaining(opens a new tab) Millennium Prize Problems posed in 2000 by the Clay Mathematics Institute, this can be related to find new fluidodynamics solutions to cardiovascular systems prediction. This paper maps the mathematical machinery of these blowup mechanisms-specifically multi-scale shear amplification and oscillatory layer cascades-directly to cardiovascular hemodynamics. By bridging Arbitrary Lagrangian--Eulerian (ALE) kinematics, Immersed Boundary (IB) singular forcing, and Carreau--Yasuda non-Newtonian rheology, we demonstrate that clinical CFD instabilities and high-shear pathological states (e.g., plaque rupture, thrombosis) represent the biological manifestation of continuum breakdown thresholds.