Geodesic
Formation of singularities for a transport equation with nonlocal velocity
Antonio Córdoba1 ; Diego Córdoba2 ; Marco A. Fontelos3
1 Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain
2 Departamento de Matemáticas, Consejo Superior de Investigaciones Científicas, 28006 Madrid, Spain
3 Departamento de Matemática Aplicada, Universidad Rey Juan Carlos, 28933 Madrid, Spain
Annals of mathematics, Tome 162 (2005) no. 3, pp. 1377-1389

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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 : 10.4007/annals.2005.162.1377

Antonio Córdoba 1 ; Diego Córdoba 2 ; Marco A. Fontelos 3

1 Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain
2 Departamento de Matemáticas, Consejo Superior de Investigaciones Científicas, 28006 Madrid, Spain
3 Departamento de Matemática Aplicada, Universidad Rey Juan Carlos, 28933 Madrid, Spain 
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Antonio Córdoba; Diego Córdoba; Marco A. Fontelos. Formation of singularities for a transport equation with nonlocal velocity. Annals of mathematics, Tome 162 (2005) no. 3, pp. 1377-1389. doi: 10.4007/annals.2005.162.1377

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