The viscosity vanishing limit and global well-posedness of the three-dimensional incompressible Navier–Stokes equations with smooth large initial data in spherical coordinates

Abstract

This paper investigates the viscosity vanishing limit and the existence and uniqueness of the global strong solution on the three-dimensional incompressible Navier–Stokes equations without swirl in spherical coordinates. We establish the global existence and uniqueness of the smooth solution to the Cauchy problem for the three-dimensional incompressible Navier–Stokes equations for the any smooth large initial data without swirl in the sense of spherical coordinates. Also, by performing the viscosity vanishing limit for the global strong solution in time to the three-dimensional incompressible Navier–Stokes equations, we prove that there exists the unique and global strong solution to the Cauchy problem for the three-dimensional incompressible Euler equation without swirl in spherical coordinates with large initial data.