Optimal transport on gas networks

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 $p = 3$.