Scattering of the Vlasov-Riesz system in the three dimensions

2024/07/24 by Huang, Wenrui, Kwon, Hyunwoo · 3 citations
#35B40 #35F50 #35Q82 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2407.16919

Abstract

We consider an asymptotic behavior of solutions to the Vlasov-Riesz system of order α in ℝ³ which is a kinetic model induced by Riesz interactions. We prove small data scattering when 1/2<α<1 and modified scattering when 1<α<1+δ for some δ>0. Moreover, we show the existence of (modified) wave operators for such a regime. To the best of our knowledge, this is the first result on the existence of modified scattering with polynomial correction in kinetic models.

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• The non-relativistic limit of scattering states for the Vlasov equation with short-range interaction potentials
• Semi-classical limit of quantum scattering states for the nonlinear Hartree equation
• Long-Time Dynamics and Modified Scattering for the Coulomb Vlasov--Hartree System

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