  In 1972, Tutte posed the $3$-Flow Conjecture: that all $4$-edge-connected
graphs have a nowhere zero $3$-flow. This was extended by Jaeger et al.(1992)
to allow vertices to have a prescribed, possibly non-zero difference (modulo
$3$) between the inflow and outflow. They conjectured that all
$5$-edge-connected graphs with a valid prescription function have a nowhere
zero $3$-flow meeting that prescription. Kochol (2001) showed that replacing
$4$-edge-connected with $5$-edge-connected would suffice to prove the $3$-Flow
Conjecture and Lov\'asz et al.(2013) showed that both conjectures hold if the
edge connectivity condition is relaxed to $6$-edge-connected. Both problems are
still open for $5$-edge-connected graphs.
  The $3$-Flow Conjecture was known to hold for planar graphs, as it is the
dual of Gr\"otzsch's Colouring Theorem. Steinberg and Younger (1989) provided
the first direct proof using flows for planar graphs, as well as a proof for
projective planar graphs. Richter et al.(2016) provided the first direct proof
using flows of the Strong $3$-Flow Conjecture for planar graphs. We prove the
Strong $3$-Flow Conjecture for projective planar graphs.
