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arXiv · 0706.1969

Formation of singularities for a transport equation with nonlocal velocity

Antonio Cordoba·Diego Cordoba·Marco A. Fontelos
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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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Antonio Cordoba, Diego Cordoba, Marco A. Fontelos. 2007-06-13. Formation of singularities for a transport equation with nonlocal velocity. https://arxiv.org/abs/0706.1969

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