Formation of singularities for a transport equation with nonlocal velocity

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/131677We study a 1D transport equation with nonlocal velocity and show the formation of singularities in finite time for a generic family of initial data. By adding a diffusion term the finite time singularity is prevented and the solutions exist globally in time.13 pages, published versionAnalysis of PDEsFormation of singularities for a transport equation with nonlocal velocitytext