Remarks about the inviscid limit of the Navier-stokes system

In this paper we prove two results about the inviscid limit of the Navier-Stokes system. The first one concerns the convergence in H ^s of a sequence of solutions to the Navier-Stokes system when the viscosity goes to zero and the initial data is in H ^s . The second result deals with the best rate of convergence for vortex patch initial data in 2 and 3 dimensions. We present here a simple proof which also works in the 3D case. The 3D case is new.