We generalize two results in the Navier-Stokes regularity theory whose proofs
rely on `zooming in' on a presumed singularity to the local setting near a
curved portion Γ⊂∂Ω of the boundary. Suppose that
u is a boundary suitable weak solution with singularity z∗=(x∗,T∗),
where x∗∈Ω∪Γ. Then, under weak background assumptions,
the L3 norm of u tends to infinity in every ball centered at x∗:
\begin{equation*} \lim_{t \to T^*_-} \lVert u(\cdot,
t)\rVert_{L_{3}\left(\Omega \cap B(x^*,r)\right)} = \infty \quad \forall r > 0.
\end{equation*} Additionally, u generates a non-trivial `mild bounded ancient
solution' in R3 or R+3 through a rescaling procedure
that `zooms in' on the singularity. Our proofs rely on a truncation procedure
for boundary suitable weak solutions. The former result is based on energy
estimates for L3 initial data and a Liouville theorem. For the latter
result, we apply perturbation theory for L∞ initial data based on
linear estimates due to K. Abe and Y. Giga