Interpolation, extrapolation, Morrey spaces and local energy control for the Navier–Stokes equations

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–Hölder spaces and $L^2$. We improve slightly his results by considering Besov–Morrey spaces and interpolation between Besov–Morrey spaces and $L^2_{\rm uloc}$.