Random electrostatic fluctuations with fixed intensity and vanishing spatial correlation produce velocity diffusion in the Vlasov-Poisson limit, proving a deterministic Vlasov-Fokker-Planck equation.
Quantitative estimates for SPDEs on the full space with transport noise and $L^p$-initial data
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For the stochastic linear transport equation with $L^p$-initial data ($1<p<2$) on the full space $\mathbb{R}^d$, we provide quantitative estimates, in negative Sobolev norms, between its solutions and that of the deterministic heat equation. Similar results are proved for the stochastic 2D Euler equations with transport noise.
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A scaling limit for Vlasov equations with electrostatic fluctuations
Random electrostatic fluctuations with fixed intensity and vanishing spatial correlation produce velocity diffusion in the Vlasov-Poisson limit, proving a deterministic Vlasov-Fokker-Planck equation.