Derivative estimates for screened Vlasov-Poisson system around Penrose-stable equilibria

2020/04/12 by Nguyen, Trinh T.
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2004.05546

Abstract

In this paper, we establish derivative estimates for the Vlasov-Poisson system with screening interactions around Penrose-stable equilibria on the phase space ℝ^d_x× ℝ_v^d, with dimension d≥ 3. In particular, we establish the optimal decay estimates for higher derivatives of the density of the perturbed system, precisely like the free transport, up to a log correction in time. This extends the recent work \citeT-R-HK by Han-Kwan, Nguyen and Rousset to higher derivatives of the density. The proof makes use of several key observations from \citeT-R-HK on the structure of the forcing term in the linear problem, with induction arguments to classify all the terms appearing in the derivative estimates.

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