Fractional Voigt-Regularization of the 3D Navier–Stokes and Euler Equations: Global Well-Posedness and Limiting Behavior Journal of Mathematical Fluid Mechanics

The Voigt regularization is a technique used to model turbulent flows, offering advantages such as sharing steady states with the Navier-Stokes equations and requiring no modification of boundary conditions; however, the parabolic dissipative character of the equation is lost. In this work we propose and study a generalization of the Voigt regularization technique by introducing a fractional power r in the Helmholtz operator, which allows for dissipation in the system, at least in the viscous case.