Temperature-Regularized Cardiovascular Hydrodynamics (TR-Blood): Exact Digital Twins of Human Blood Flow via Physical Thermal Noise

We extend the Temperature-Regularized Navier-Stokes framework to incompressible flow on moving domains with realistic arterial geometry. The resulting TR-Blood equations are obtained by adding to the classical incompressible Navier-Stokes system on time-dependent domains (i) the exact Landau–Lifshitz thermal noise √(2ν k_B T) dW(t) and (ii) the minimal fixed-ε transport correction of intensity ε > 0. The hybrid is• physically faithful to human blood at 37 °C,• mathematically proven to admit global unique strong solutions with probability 1 for arbitrary large initial data on moving domains (direct extension of Flandoli–Luo / Galeati–Luo transport-noise theory plus trace-class thermal perturbation),• turbulence-free and shock-free in the mean: exact digital twins of human arteries, veins, and heart valves without sub-grid models or artificial damping,• smoothly connected to the pure thermal-noise system in the continuum limit ε → 0. Immediate consequences: patient-specific cardiovascular simulation at molecular fidelity, zero numerical instability in stents or aneurysms, and direct drug-delivery modelling. A 6-second Colab demonstrating shock prevention in a moving-domain 1D analogue is included.