  We consider the problem of the strong convergence, as the viscosity goes to
zero, of the solutions to the three-dimensional evolutionary Navier-Stokes
equations under a Navier slip-type boundary condition to the solution of the
Euler equations under the zero flux boundary condition. In spite of the
arbitrarily strong convergence results proved in the flat boundary case, see
[4], it was shown in reference [5] that the result is false in general, by
constructing an explicit family of smooth initial data in the sphere, for which
the result fails. Our aim here is to present a more general, simpler and
incisive proof. In particular, counterexamples can be displayed in arbitrary,
smooth, domains. As in [5], the proof is reduced to the lack of a suitable
persistence property for the Euler equations. This negative result is proved by
a completely different approach.
