On the inviscid limit of the 2D Euler equations with vorticity along the (LMO)_ scale

In a recent paper [5], the global well-posedness of the twodimensional Euler equation with vorticity in L1 ∩ LBMO was proved, where LBMO is a Banach space which is strictly imbricated between L and BMO. In the present paper we prove a global result of inviscid limit of the Navier-stokes system with data in this space and other spaces with the same BMO flavor. Some results of local uniform estimates on solutions of the Navier-Stokes equations, independent of the viscosity, are also obtained.