学术报告(杨东成 2026.10.14)
Ionic KdV structure in weakly collisional plasmas
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.

