Formation of singularities for a transport equation with nonlocal velocity

Abstract

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.

Authors

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