Inviscid limit for axisymmetric Navier-Stokes system

Abstract

We are interested in the global well posedness of the axisymmetric Navier-Stokes system with initial data belonging to the critical Besov spaces ${B}_{p, 1}^{1+\frac{3}{p}}$. We obtain uniform estimates of the viscous solutions $(v_\nu)$ with respect to the viscosity in the spirit of the work [2] concerning the axisymmetric Euler equations. We provide also a strong convergence result in the $L^p$ norm of the viscous solutions $(v_\nu)$ to the Eulerian one $v$.