54 citations · 237 across the 25 of their papers we have counts for
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The Semi-Classical Limit from the Dirac Equation with Time-Dependent External Electromagnetic Field to Relativistic Vlasov Equations
François Golse, Nikolai Leopold, Norbert J. Mauser +2
We prove the mathematically rigorous (semi-)classical limit of the Dirac equation with time-dependent external electromagnetic field to relativistic Vlasov equations…
Existence and stability of weak solutions of the Vlasov--Poisson system in localized Yudovich spaces
Gianluca Crippa, Marco Inversi, Chiara Saffirio +1
We consider the Vlasov--Poisson system both in the repulsive (electrostatic potential) and in the attractive (gravitational potential) cases. In our first main theorem, we prove th…
Uniqueness criteria for the Vlasov--Poisson system and applications to semiclassical analysis
Laurent Lafleche, Chiara Saffirio
We review some uniqueness criteria for the Vlasov--Poisson system, emerging as corollaries of stability estimates in strong or weak topologies, and show how they serve as a guideli…
On the Rate of Convergence in the Limit from the Hartree to the Vlasov$\unicode{x2013}$Poisson Equation
Jacky J. Chong, Laurent Lafleche, Chiara Saffirio
Using a new stability estimate for the difference of the square roots of two solutions of the Vlasov$\unicode{x2013}$Poisson equation, we obtain the convergence in the norm o…
Global-in-time Semiclassical Regularity for the Hartree-Fock Equation
Jacky J. Chong, Laurent Lafleche, Chiara Saffirio
For arbitrarily large times , we prove the uniform-in- propagation of semiclassical regularity for the solutions to the Hartree$\unicode{x2013}$Fock equation with singu…
From many-body quantum dynamics to the Hartree-Fock and Vlasov equations with singular potentials
Jacky J. Chong, Laurent Lafleche, Chiara Saffirio
We obtain the combined mean-field and semiclassical limit from the -body Schrödinger equation for fermions interacting via singular potentials. To obtain the result, we first pr…
Lagrangian solutions to the Vlasov-Poisson system with a point charge
Gianluca Crippa, Silvia Ligabue, Chiara Saffirio
We consider the Cauchy problem for the repulsive Vlasov-Poisson system in the three dimensional space, where the initial datum is the sum of a diffuse density, assumed to be bounde…