  In a recent paper [5], the global well-posedness of the two-dimensional Euler
equation with vorticity in \mbox{$L^1\cap LBMO$} was proved, where $ LBMO$ is a
Banach space which is strictly imbricated between \mbox{$L^\infty$} 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.
