Global regularity of the axisymmetric Navier–Stokes model with logarithmically supercritical dissipation

In this paper, we investigate the global regularity of a generalized axisymmetric model which was proposed in Hou and Lei (2009) [4] to study the role of convection in incompressible Navier–Stokes equations. By introducing a logarithmically supercritical dissipation whose symbol satisfies m(ξ)≥|ξ|74g(|ξ|) for all sufficiently large |ξ||ξ| and some nondecreasing function g(s)g(s) satisfying ∫1+∞dssg4(s)=+∞, we obtain the global regularity of the generalized axisymmetric Navier–Stokes model.