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arXiv:0706.1969 [math.AP]AbstractReferencesReviewsResources

Formation of singularities for a transport equation with nonlocal velocity

Antonio Cordoba, Diego Cordoba, Marco A. Fontelos

Published 2007-06-13Version 1

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.

Comments: 13 pages, published version
Journal: Ann. of Math. (2) 162 (2005), no. 3, 1377--1389
Categories: math.AP
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