Global stability of large solutions for the Navier-Stokes equations with Navier boundary conditions

We prove global stability of strong large solutions for the 3D incompressible Navier-Stokes equations with Navier slip boundary conditions. This result is obtained under an integrable property that depends on these slip conditions. In addition, we show that strong helical solutions are global in time. Combining the latter with the stability result, we provide a class of 3D global large solutions with perturbations of helical vector-fields as initial data.