Inviscid limit for the two-dimensional Navier-Stokes system in a critical Besov space

In a recent paper [12], Vishik proved the global wellposedness of the two-dimensional Euler equation in the critical Besov space B 2,1. In the present paper we prove that the Navier-Stokes system is globally well-posed in B 2,1, with uniform estimates on the viscosity. We prove also a global result of inviscid limit. The convergence rate in L is of order ν.