  This paper models gas networks as metric graphs, with isothermal Euler
equations at the edges, Kirchhoff's law at interior vertices and
time-(in)dependent boundary conditions at boundary vertices. For this setup, a
generalized $p$-Wasserstein metric in a dynamic formulation is introduced and
utilized to derive $p$-Wasserstein gradient flows, specifically focusing on the
non-standard case $p = 3$.
