Zu Chongzhi Research Seminar

Date and Time (China standard time): Monday, May 12, 10:00 am – 11:00 am

Location: WDR 1007

Zoom: 972 2412 7261, Passcode: dkumath

Title: Asymptotic stability of the Boltzmann equation in an infinite layer

Speaker: Hongxu Chen

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.

Bio: I obtained my Ph.D. in 2022 from the University of Wisconsin-Madison. I am currently a postdoctoral fellow at The Chinese University of Hong Kong. My research focuses on partial differential equations, in particular, the kinetic equation and fluid equation.