Strong chromatic index of subcubic planar multigraphs

The strong chromatic index of a multigraph is the minimum $k$ such that the edge set can be $k$-colored requiring that each color class induces a matching. We verify a conjecture of Faudree, Gy\'{a}rf\'{a}s, Schelp and Tuza, showing that every planar multigraph with maximum degree at most 3 has strong chromatic index at most 9, which is sharp.