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Hypocoercivity and Uniform Regularity for the Vlasov--Poisson--Fokker--Planck System with Uncertainty and Multiple Scales
We study the Vlasov--Poisson--Fokker--Planck system with uncertainty and multiple scales. Here the uncertainty, modeled by random variables, enters the solution through initial data, while the multiple scales lead the system to its high-field or parabolic regimes. With the help of proper Lyapunov-type inequalities, under some mild conditions on the initial …