Global Regularity and Scale-Selective Ibaguner-Euler Damped Navier-Stokes Flows in 3D

We study a modified three-dimensional Navier-Stokes system with a scale-selective nonlinear damping term enforcing the Ibaguner-Euler constant 1/e as the energy of the large scales. We rigorously prove global existence and uniqueness of smooth solutions for all divergence-free initial data in H^1 (T^3), construct a finite-dimensional global attractor, and demonstrate exponential convergence of the low-mode energy to 1/e. The model preserves small-scale turbulent interactions while controlling blow-up mechanisms, providing a mathematically and physically meaningful regularization of 3D incompressible flows.