  We construct weak solutions to the Navier-Stokes inequality, $$ u\cdot
\left(\partial_t u -\nu \Delta u + (u\cdot \nabla) u +\nabla p \right) \leq 0
$$ in $\mathbb{R}^3$, which blow up at a single point $(x_0,T_0)$ or on a set
$S \times \{T_0 \}$, where $S\subset \mathbb{R}^3$ is a Cantor set whose
Hausdorff dimension is at least $\xi$ for any preassigned $\xi\in (0,1)$. Such
solutions were constructed by Scheffer, Comm. Math. Phys., 1985 & 1987. Here we
offer a simpler perspective on these constructions. We sharpen the approach to
construct smooth solutions to the Navier-Stokes inequality on the time interval
$[0,1]$ satisfying the "approximate equality" $$ \left\| u\cdot
\left(\partial_t u-\nu \Delta u + (u\cdot \nabla) u +\nabla p \right)
\right\|_{L^\infty}\leq \vartheta, $$ and the "norm inflation" $\| u(1)
\|_{L^\infty} \geq \mathcal{N} \| u(0) \|_{L^\infty}$ for any preassigned
$\mathcal{N}>0$, $\vartheta >0$. Furthermore we extend the approach to
construct a weak solution to the Euler inequality $$u\cdot \left(\partial_t u+
(u\cdot \nabla) u +\nabla p \right) \leq 0, $$ which satisfies the approximate
equality with $\nu =0$ and blows up on the Cantor set $S\times \{T_0 \}$ as
above.
