Around Boltzmann equation
The aim of workshop is to bring together young experts to share their recent research results on the mathematical analysis of Boltzmann equation and related kinetic models. Undergraduate/Graduate students and postdocs are particularly encouraged to participate in. Please send an email to ypchoi at yonsei.ac.kr if you need further information.
Venue: Science Hall 225, Yonsei University
Registration (closed)
Confirmed Participants
Jinwoo Jang (Pohang University of Science and Technology)
Donghyun Lee (Pohang University of Science and Technology)
Seok-Bae Yun (Sungkyunkwan University)
Opening
Donghyun Lee (Pohang University of Science and Technology)
Title: Introduction to the Boltzmann equation and its convergence to equilibrium
Abstract: We briefly introduce basic of the Boltzmann equation. In particular, key mechanism and low regularity approach for trends to equilibrium will be discussed.
Lunch & Coffee
Jinwoo Jang (Pohang University of Science and Technology)
Title: Vanishing angular singularity limit to the hard-sphere Boltzmann equation
Abstract: In this talk we study Boltzmann's collision kernel for inverse power law interactions $U_s(r)=1/r^{s-1}$ for $s>2$ in dimension $d=3$. We prove the limit of the non-cutoff kernel to the hard-sphere kernel and give precise asymptotic formulas of the singular layer near $\theta\simeq 0$ in the limit $s\to \infty$. Consequently, we show that solutions to the homogeneous Boltzmann equation converge to the respective solutions.
Coffee
Seok-Bae Yun (Sungkyunkwan University)
Title: Introduction to BGK models
Abstract: The Boltzmann equation is fundamental but not practical. The complicated structure of the collision operator requires large computation resources which even modern computers cannot handle efficiently. BGK model is a model equation of the Boltzmann equation that reproduces reliable results at much lower computational costs. In this lecture, we introduce various BGK models, study the basic properties of the model, and review mathematical results. If time allows, we consider an argument to obtain the existence of solutions to a BGK model.
Closing
Dinner
Young-Pil Choi (Yonsei University) and Byung-Hoon Hwang (Sangmyung University)
This scientific event is sponsored by National Research Foundation of Korea and BK21 Yonsei Mathematical Sciences and Computation.