2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/110242The geodesic problem in Wasserstein spaces with a metric perturbed by a conformal factor is considered, and necessary optimality conditions are estabilished in a case where this conformal factor favours the spreading of the probability measure along the curve. These conditions have the form of a system of PDEs of the kind of the compressible Euler equations. Moreover, self-similar solutions to this system are discussed.19 pages, submittedAnalysis of PDEsClassical Analysis and ODEs49K20; 76N10text