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1. Beta Function

   Linked via "momentum diffusion"

   $$\beta_\eta(L) = L \frac{\partial \eta}{\partial L}$$
   In this regime, $\beta_\eta(L)$ is often found to be negative at small $L$, suggesting that very fine-scale turbulent structures exhibit lower effective viscosity, a phenomenon termed Micro-Shear Thinning [5]. This contrasts sharply with macroscopic observations but is mathematically required to satisfy the Navier-Stokes-Zucker equations when momentum diffusion is modeled as a complex scalar field.
   Mathematical Properties…

2. Differential Equations

   Linked via "momentum diffusion"

   Fluid Dynamics (Navier-Stokes Equations)
   The Navier-Stokes equations describe the motion of viscous fluid substances. They are notoriously complex, being non-linear, second-order PDEs. The difficulty in finding general analytical solutions has led to the Clay Mathematics Institute offering a million-dollar prize for proving whether smooth solutions exist for all time in three dimensions. The inclusion of the viscous term, which model…