A study on the global regularity for a model of the 3D axisymmetric Navier–Stokes equations

This paper investigates the global regularity issue concerning a model equation proposed by Hou and Lei (2008) [9] to understand the stabilizing effects of the nonlinear terms in the 3D axisymmetric Navier–Stokes and Euler equations. We establish the global regularity of a generalized version of their model with a fractional Laplacian when the fractional power satisfies an explicit condition. This condition is exactly the same as in the case of the 3D generalized Navier–Stokes equations and is due to the balance between a more regular nonlinearity and a less effective (five-dimensional) Laplacian.