Damped-vorticity maximum estimate
= Damped-vorticity maximum estimate
For a steady damped vorticity equation with $\gamma>0$, divergence-free transport, and bounded forcing, multiplication by $\omega|\omega|^{q-2}$ gives $\gamma\|\omega\|_q\leq\|g\|_q$. Sending $q$ to infinity yields
$$
\gamma\|\omega\|_\infty\leq\|g\|_\infty.
$$