Non-uniqueness of signed measure-valued solutions to the continuity equation in presence of a unique flow

Paolo Bonicatto, Nikolay A. Gusev

We consider the continuity equation ${\partial }_t{\mu }_t+\mathrm{div}(b{\mu }_t)=0$, where $\{{\mu }_t{\}}_{t\in \mathbb{R}}$ is a measurable family of (possibily signed) Borel measur…