报告题目：Global well-posedness of Vlasov-Poisson-Boltzmann system with neutral initial data and small relative entropy

报告人：熊杭博士，湘潭大学

报告时间：2024年11月1日（周五）14:00-15:00

报告地点：22-322

报告摘要：The dynamics of dilute plasma particles such as electrons and ions can be modeled by the fundamental two species Vlasov-Poisson-Boltzmann (VPB) system which describes mutual interactions of plasma particles through collisions in the self-induced electric field. In this paper, we are concerned with global well-posed theory of mild solutions to this system. We established the global existence and uniqueness of mild solutions to the two species VPB system in the torus for a class of initial data with bounded time-velocity-weighted $L^{\infty}$ norm under nearly neutral condition and some smallness condition on $L^1_xL^\infty_v$ norm with time-velocity-weight as well as  defect mass, energy and entropy so that the initial data  allow  large amplitude oscillations. Moreover, the large time behavior of solutions in $W^{1, \infty}_{x,v}$ norm with exponential decay rates of convergence is also studied. The proof is based on a new logarithmic estimate in potential analysis, the introduction of the free streaming condition on the characteristics and a  $L^\infty_xL^1_{v}\capL^\infty_{x,v}$-method with time-velocity- exponential weights.

报告人简介：熊杭，现为湘潭大学教师。2020年12月博士毕业于华中科技大学，2021年1月-2024年6月，曾在中国科学院数学与系统科学研究院从事博士后研究工作。主要从事Boltzmann方程及其相关动理学模型适定性问题的研究。曾主持中国博士后科学基金特别资助项目1项，中国博士后科学基金面上项目1项，在JDE、JMP期刊上发表论文。

邀请人：非线性分析与PDE团队