学术报告

题      目：KdV limit for the Vlasov-Poisson-Landau system

报  告  人：杨东成  副教授  (邀请人：喻洪俊 )

                                    华南理工大学

时      间：5月15日  15：00-15：45

地     点：数科院东楼401

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等上发表学术论文10余篇。

摘      要：

        In this talk we are concerned with the fluid limit to KdV equations for the one-dimensional Vlasov-Poisson-Landau system which describes the dynamics of ions in plasma with the electron density determined by the self-consistent electric potential through the so-called Boltzmann relation. Formally, it is well known that as the Knudsen number ϵ→0 the Vlasov-Poisson-Landau system in the compressible scaling converges to the Euler-Poisson equations which further under the Gardner-Morikawa transformation (t,x)→(δ^(3/2) t,δ^(1/2) (x-√(8/3) t))

converge to the KdV equations as the parameter δ→0. We construct smooth solutions of the correspondingly rescaled Vlasov-Poisson- Landau system over an arbitrary finite time interval  that can converge uniformly to smooth solutions of the KdV equations as ϵ→0 and δ→0 simultaneously under an extra condition ϵ^(2/3)≤δ≤ϵ^(2/5). Moreover, the explicit rate of convergence in δ is also obtained.

        欢迎老师、同学们参加、交流！