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math.AP2024
A blow-down mechanism for the Landau-Coulomb equation
Maria Pia Gualdani, Raphael Winter
We investigate the Landau-Coulomb equation and show an explicit blow-down mechanism for a family of initial data that are small-scale, supercritical perturbations of a Maxwellian f…
math.AP2023
Existence and non-uniqueness of stationary states for the Vlasov-Poisson equation on subject to attractive background charges
Raphael Winter
We prove the existence of stationary solutions for the density of an infinitely extended plasma interacting with an arbitrary configuration of background charges. Furthermore, we s…
math.AP2022
The grazing collisions limit from the linearized Boltzmann equation to the Landau equation for short-range potentials
Corentin Le Bihan, Raphael Winter
The Landau equation and the Boltzmann equation are connected through the limit of grazing collisions. This has been proved rigorously for certain families of Boltzmann operators co…