Abstract:
The talk will be devoted to the Cauchy problem for the continuity equation with a nearly incompressible BV vector field.
This class of vector fields is related to the theory of hyperbolic conservation laws, and it was
studied by R.J. DiPerna, P.-L. Lions, L. Ambrosio and many others. We will discuss some new sufficient conditions
for uniqueness of weak solutions, obtained in collaboration with S. Bianchini and P. Bonicatto.