Formation of singularities for a transport equation with nonlocal velocity

Details Formation of singularities for a transport equation with nonlocal velocity Formation of singularities for a transport equation with nonlocal velocity

2007-06-13

arxiv.org/abs/0706.1969v1

Ann. of Math. (2) 162 (2005), no. 3, 1377--1389

Mathematics

Analysis of PDEs

13 pages, published version

Scientific paper

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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