报告人：刘双乾教授

报告时间：2025年12月15日下午15:00

腾讯会议号：175-839-671

报告摘要：In this talk, I will report our recent study on the non-cutoff Vlasov–Poisson–Boltzmann (VPB) system. We prove global existence of smooth solutions near Maxwellians for the non-cutoff VPB system in the weakly collisional regime. To address the weak dissipation of the non-cutoff linearized Boltzmann operator, we develop a refined velocity-weighted energy framework combined with vector-field techniques to control the transport term, nonlinear collisions, and the self-consistent electric field. This approach yields uniform-in-time bounds, captures enhanced dissipation of the solution, and establishes Landau damping for both the density and electric field, providing the first global-in-time result of this type for the non-cutoff Vlasov–Poisson–Boltzmann system. Our approach is inspired by the recent work of Chaturvedi-Luk-Nguyen ({\it J. Amer. Math. Soc.} {\bf 36} (2023), no. 4, 1103--1189.)

报告人简介：刘双乾，华中师范大学数学与统计学院教授、博士生导师、副院长。主要研究基本物理模型的偏微分方程，涉及稀薄气体理论的动理学方程、等离子体的Landau方程、及相关的流体力学方程等领域；在动理学方程的整体适定性、动理学方程的流体动力学极限、以及Boltzmann方程剪切流的稳定性等问题上取得了一系列成果；在Comm. Pure Appl. Math.、 J. Eur. Math. Soc.、 Comm. Math. Phys.、 Arch. Ration. Mech. Anal.、Trans. Amer. Math. Soc.等国际著名数学期刊上发表论文60余篇。2023年获国家杰出青年科学基金资助。