57 citations · 413 across the 51 of their papers we have counts for
3 papers · 2 filters
On the Lagrangian structure of transport equations: the Vlasov-Poisson system
Luigi Ambrosio, Maria Colombo, Alessio Figalli
The Vlasov-Poisson system is a classical model in physics used to describe the evolution of particles under their self-consistent electric or gravitational field. The existence of…
Renormalized solutions to the continuity equation with an integrable damping term
Maria Colombo, Gianluca Crippa, Stefano Spirito
We consider the continuity equation with a nonsmooth vector field and a damping term. In their fundamental paper, DiPerna and Lions proved that, when the damping term is bounded in…
Existence and uniqueness of maximal regular flows for non-smooth vector fields
Luigi Ambrosio, Maria Colombo, Alessio Figalli
In this paper we provide a complete analogy between the Cauchy-Lipschitz and the DiPerna-Lions theories for ODE's, by developing a local version of the DiPerna-Lions theory. More p…