The Vlasov-Poisson-Boltzmann System
with a Repulsive Potential Near Vacuum
报告专家：熊林杰 教授（湖南大学）
报告时间：10月18日（周六）10:20-11:00
报告地点：国家天元数学西南中心516
报告摘要：
The problem of very soft potential cases $\gamma \in (-3,-2]$ for the Vlasov–Poisson-Boltzmann system near vacuum has remained unresolved in Guo's work [Comm. Math. Phys.218(2001), no.2, 293–313.] for over two decades, limited by the decay of spatial density. We provide a positive answer to this problem with the assistance of an external potential in the present work. Specifically, by employing optimal decay estimates derived by A. Velozo Ruiz and R. Velozo Ruiz [Comm. Math. Phys. 405 (2024), no. 3, Paper No. 80, 45 pp.] using a commuting vector field approach, we construct global classical solutions for the Vlasov–Poisson-Boltzmann system with the repulsive potential $\Phi(x) = \frac{-|x|^2}{2} $ for the whole range of cutoff soft potentials $\gamma \in (-3,0)$.
专家简介：
熊林杰，湖南大学数学学院教授，博士生导师，博士毕业于武汉大学，曾在法国巴黎综合理工访问一年，主要从事Boltzmann方程及其相关动理学模型的数学理论研究，在平衡态附近Vlasov-Poisson-Boltzmann方程的经典解构造，Boltzmann方程的扩散极限等方面做出一些工作，相关结果发表在SIAM，JFA，JDE, Sci. China Math.等著名学术期刊，主持国家自然科学基金两项，参与国家自然科学基金重点项目一项。
邀请人：程建峰、何躏
