勷勤数学•专家报告

题      目：Ionic KdV structure in weakly collisional plasmas

报  告  人： 杨东成 副教授  (邀请人：喻洪俊)

                                       华南理工大学

时      间： 10月31日  16：30-17:30

地     点：数科院东楼二楼会议室

报告人简介:

        杨东成副教授，现工作在华南理工大学数学学院， 从事动理学方程等偏微分方程的数学理论研究，已在国际顶级期刊 Communications in Mathematical Physics， Archive for Rational Mechanics and Analysis, J. Math. Pures Appl. 等上发表学术论文10余篇。

摘      要：

       In this talk, we consider the one-dimensional ions dynamics in weakly collisional plasmas governed by the Vlasov-Poisson-Landau system under the Boltzmann relation with the small collision frequency $\nu>0$. It is observed in physical experiments that the interplay of nonlinearities and dispersion may lead to the formation of ion acoustic solitons that are described by the Korteweg-de Vries equation. To capture the ionic KdV structure in the weak-collision regime, we study the combined cold-ions limit and long-wave limit of the rescaled VPL system depending on another small scaling parameter $\eps>0$. The main goal is to justify the uniform convergence of the VPL solutions to the KdV solutions over any finite time interval as $\eps\to 0$ under restriction that $\eps^{3/2}\lesssim \nu \lesssim \eps^{1/2}$. The KdV profiles, in particular including both velocity field and electric potential, can have large amplitude. The proof is based on the energy method near local Maxwellians for making use of the Euler-Poisson dynamics under the long-wave scaling.

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