368 citations · 558 across the 22 of their papers we have counts for
24 papers
Variational derivation of the homogeneous Boltzmann equation
Giada Basile, Dario Benedetto, Carlo Orrieri
We introduce a variational formulation of the homogeneous Boltzmann equation, with hard-sphere cross section, which selects the unique energy conserving solution. We prove that thi…
Scattering problem for Vlasov-type equations on the -dimensional torus with Gevrey data
Dario Benedetto, Emanuele Caglioti, Antoine Gagnebin +2
In this article, we consider Vlasov-type equations describing the evolution of single-species type plasmas, such as those composed of electrons (Vlasov-Poisson) or ions (screened V…
Propagation of chaos and hydrodynamic description for topological models
Dario Benedetto, Thierry Paul, Stefano Rossi
In this work, we study the deterministic Cucker-Smale model with topological interaction. Focusing on the solutions of the corresponding Liouville equation, we show that propagatio…
Microcanonical phase transitions for the vortex system
Dario Benedetto, Emanuele Caglioti, Margherita Nolasco
We consider the Microcanonical Variational Principle for the vortex system in a bounded domain. In particular we are interested in the thermodynamic properties of the system in dom…
Asymptotic probability of energy increasing solutions to the homogeneous Boltzmann equation
Giada Basile, Dario Benedetto, Lorenzo Bertini +1
Weak solutions to the homogeneous Boltzmann equation with increasing energy have been constructed by Lu and Wennberg. We consider an underlying microscopic stochastic model with bi…
Mean-field limit for particle systems with topological interactions
Dario Benedetto, Emanuele Caglioti, Stefano Rossi
The mean-field limit for systems of self-propelled agents with topological interaction cannot be obtained by means of the usual Dobrushin approach. We get a result on this directio…