报告题目：The Global Well-Posedness of the Relativistic Boltzmann Equation with Diffuse Reflection Boundary Condition in Bounded Domains

报 告 人：王勇副研究员（中国科学院数学与系统科学研究院）

报告时间：2023年6月25日  10:00-11:00

报告地点：理学院五楼数学中心528报告厅

报告摘要：

The relativistic Boltzmann equation in bounded domains has been widely used in physics and engineering, for example, Tokamak devices in fusion reactors. In spite of its importance, there has, to the best of our knowledge, been no mathematical theory on the global existence of solutions to the relativistic Boltzmann equation in bounded domains. In the present paper, assuming that the motion of single-species relativistic particles in a bounded domain is governed by the relativistic Boltzmann equation with diffuse reflection boundary conditions of non- isothermal wall temperature of small variations around a positive constant, and regarding the speed of light $\mathfrak{c}$ as a large parameter, we first construct a unique non-negative stationary solution $F_ {*}$, and further establish the dynamical stability of such stationary solution with exponential time decay rate. We point out that the $L ^ {\infty } $-bound of perturbations for both steady and non-steady solutions are independent of the speed of light $ mathfrak{c}$，and such uniform in $\mathfrak {c} $ estimates will be useful in the study of Newtonian limit in the future.

报告人简介：

王勇，中科院数学与系统科学研究院副研究员。2012年博士毕业于中科院数学与系统科学研究院，曾获中科院数学与系统科学研究院“重要科研进展奖”、入选中科院数学与系统科学研究院“陈景润未来之星”计划、入选中科院青年创新促进会，2020年获国家优秀青年科学基金资助。主要研究可压缩Euler方程、可压缩Navier-Stokes方程、Boltzmann方程等方程的适定性和流体动力学极限。目前已经在Communications on Pure and Applied Mathematics，Advances in Mathematics（2篇），Archive for Rational Mechanics and Analysis（6篇）和SIAM Journal on Mathematical Analysis（9篇）等国际著名刊物上接受和发表学术论文30余篇。