Formation of singularities for a transport equation with nonlocal velocity

Autores: Diego Córdoba Gazolaz , Marco Antonio Fontelos , Antonio Córdoba Barba
Localización: Annals of mathematics, ISSN 0003-486X, Vol. 162, Nº 3, 2005, págs. 1375-1387
Idioma: inglés
DOI: 10.4007/annals.2005.162.1377
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Resumen
- 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.