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.
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CITATION STYLE
APA
Córdoba, A., Córdoba, D., & Fontelos, M. A. (2005). Formation of singularities for a transport equation with nonlocal velocity. Annals of Mathematics, 162(3), 1377–1389. https://doi.org/10.4007/annals.2005.162.1377
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