Formation of singularities for a transport equation with nonlocal velocity

Pages 1377-1389 from Volume 162 (2005), Issue 3 by Antonio Córdoba, Diego Córdoba, Marco A. Fontelos

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.

DOI
https://doi.org/10.4007/annals.2005.162.1377
MR
2179734
zbMATH
1101.35052
Milestones
Received: 24 May 2004
Published online: 1 March 2009

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