中科院数学与系统科学研究院
数学研究所
学术报告
偏微分方程研讨班
报告人：Klaus Widmayer（University of Zurich）
题 目：On the stability of a point charge for the Vlasov-Poisson system
时 间：2022.09.22（星期四）21:00-22:00
地 点：Zoom ID: 924 888 5804 Passcode: AMSS2022
Join Zoom Meeting :
https://us06web.zoom.us/j/9248885804?pwd=OXg2VDhBT0pxRkd1Z3RJS0NFMnRDdz09
摘 要：A Dirac mass is a particularly simple yet relevant equilibrium of the (repulsive) Vlasov-Poisson equations. This talk addresses the question of its stability in the repulsive setting: we capture the precise asymptotic dynamics of solutions which start as small, smooth and suitably localized perturbations of a point charge. Our analysis builds on the Hamiltonian/symplectic structure of the equations, and makes use of an exact integration of the linearized equation through angle-action coordinates. This allows us to obtain optimal decay estimates and reveals a modified scattering dynamic.
This is joint work with Jiaqi Yang (ICERM) and Benoit Pausader (Brown University).
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