Đề tài " Formation of singularities for a transport equation with nonlocal velocity "

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. 1. Introduction In this paper we study the nature of the solutions to the following class of equations (1.1)