  Barker recently proved new weak-strong uniqueness results for the
Navier-Stokes equations based on a criterion involving Besov spaces and a proof
through interpolation between Besov-H{\"o}lder spaces and L 2. We improve
slightly his results by considering Besov-Morrey spaces and interpolation
between Besov-Morrey spaces and L 2 uloc. Let u 0 a divergence-free vector
field on R 3. We shall consider weak solutions to the Cauchy initial value
problem for the Navier-Stokes equations which satisfy energy estimates. The
differential Navier-Stokes equations read as $\partial$ t u + u. $\nabla$ u =
$\Delta$ u -- $\nabla$p div u = 0 u(0, .) = u 0 *
