Formation of singularities for a transport equation with nonlocal velocity


We 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.


Antonio Córdoba

Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain

Diego Córdoba

Departamento de Matemáticas, Consejo Superior de Investigaciones Científicas, 28006 Madrid, Spain

Marco A. Fontelos

Departamento de Matemática Aplicada, Universidad Rey Juan Carlos, 28933 Madrid, Spain