Formation of singularities for a transport equation with nonlocal velocity

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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.
13 pages, published version

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Analysis of PDEs

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http://salesiana.dossiersoluciones.com/handle/123456789/131677

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0706.1969
 http://arxiv.org/abs/0706.1969
 Ann. of Math. (2) 162 (2005), no. 3, 1377--1389

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arXiv