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Scattering problem for Vlasov-type equations on the d-dimensional torus with Gevrey data

Dario Benedetto, Emanuele Caglioti, Antoine Gagnebin, Mikaela Iacobelli, Stefano Rossi

16/5/24 Published in : arXiv:2405.10182

In this article, we consider Vlasov-type equations describing the evolution of single-species type plasmas, such as those composed of electrons (Vlasov-Poisson) or ions (screened Vlasov-Poisson/Vlasov-Poisson with massless electrons). We solve the final data problem on the torus \mathbb{T}^d, d≥1, by considering asymptotic states of regularity Gevrey-\frac{1}{γ} with γ>\frac13, small perturbations of homogeneous equilibria satisfying the Penrose stability condition. This extends to the Gevrey perturbative case, and to higher dimension, the scattering result in analytic regularity obtained by E. Caglioti and C. Maffei in [14], and answers an open question raised by J. Bedrossian in arXiv:2211.13707.

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Phase I & II research project(s)

  • Statistical Mechanics

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  • Differential equations of Mathematical Physics

SLE and its partition function in multiply connected domains via the Gaussian Free Field and restriction measures

Topologically Robust Quantum Network Nonlocality

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