Asymptotic stability of the Boltzmann equation in an infinite layer

发布时间：2025-04-27 来源：威廉希尔williamhill 浏览次数：

Speaker:	陈泓旭	DateTime:	2025年4月29日（周二）上午10：30-11：30
Brief Introduction to Speaker: 香港中文大学		Place:	国交2号楼201
Abstract:In this talk, I will discuss the Boltzmann equation in an infinite layer $R^2\times (-1,1)$, with the diffuse reflection boundary condition. Generally, the kinetic equation exhibits singularities near the boundary, one can not directly apply high order energy methods. We propose a new approach that employs the Fourier transform in the horizontal direction, combined with an $L^2-L^\infty$ argument in the vertical direction. Our result demonstrates that the solutions decay in time at the same polynomial rate as the two-dimensional heat equation.