The purpose of the summer school is to introduce graduate students to fundamental results on the kinetic theory and the fluid dynamics, with special emphasis on (1) the relation between kinetic theory and fluid dynamics; (2) the dispersive water wave; (3) the transonic flows. These topics have long research history. In this summer school, the speakers will give comprehensive accounts on the aforementioned topics and introduce some interesting open problems.
Organizers
Chun-Hsiung Hsia (National Taiwan University and NCTS),
Jerry L. Bona (University of Illinois at Chicago and National Taiwan University),
Kung-Chien Wu (National Cheng Kung University).
Kazuo Aoki, Kyoto University and National Cheng Kung University.
From kinetic theory to fluid dynamics
The relationship between kinetic theory of gases and fluid dynamics has been one of important research topics in both mathematics and physics since the early 20th century. In this course, some aspects of this relationship are discussed mainly from the standpoint of physical and formal analysis. Specifically, we start with a summary of the Boltzmann equation and then explain the classical Chapman-Enskog and Hilbert expansions. The Chapman-Enskog expansion leads to the compressible Navier-Stokes equations. The slip boundary conditions for the compressible Navier-Stokes equations are also discussed. Furthermore, we show that, depending on the physical situation, fluid-dynamic equations of types other than traditional equations, such as the Euler and Navier-Stokes equations, can be derived from the Boltzmann equation. We mainly discuss the results based on formal analysis but also touch on rigorous mathematical results when necessary.
Jerry L. Bona, University of Illinois at Chicago and National Taiwan University,
Theory and Application of Dispersive Wave Equations
In the first half of the 20th century, the theory of partial differential equations revolved around elliptic, hyperbolic and parabolic type equations. In the second half of the century, a new type of equation appeared on the scene, namely dispersive equations. Arising first in applications, these equations have taken a prominent place in the modern theory of partial differential equations. At the same time, the number of applications of such equations has grown rapidly as well.
This set of lectures aims to introduce some of the modern mathematical theory that has emerged as well as survey a selection of the many real-world situations where dispersive equations arise as models for the phenomena in question.
Please note that registration is free, but required. The lecture series will be aimed at the graduate-student audience for whom the lecture series is designed.
Financial Support: We are pleased to offer accommodations at a Youth Hostel (with separate shared rooms for males and females) for a limited number of summer school participants. Due to the limited availability of support, applicants must submit their CV and a recommendation letter. Applications will be carefully reviewed, with priority given to those who demonstrate strong academic qualifications and whose research aligns closely with the summer school themes.
Please note that the deadline for registration is 10th April 2025.
For further information and questions about the summer school, please contact :
The summer school will take place in Chee-Chun Leung Cosmology Hall, National Taiwan University.
All lectures will be held in Room 505.
Week 1
June 2nd - June 6th
10:00 - 12:00 lecture
12:00 - 13:30 lunch
13:30 - 15:30 Free discussion : Lecturers share academic experience with participants and QA in a casual way.
*Prof. Zhouping Xin will be unable to attend and lecture at the Summer School due to health reasons. We will arrange alternative activities in place of his sessions.
Week 2
June 9th - June 11th
We are organizing the 2025 NCTS International Conference on PDEs in the afternoons on June 10 and 11. We schedule 3 talks each afternoon. There will be 10 talks at the conference in total.
More information about the 2025 NCTS International Conference on PDEs
June 9
10:00 - 12:00 lecture (Prof. Jerry L. Bona)
12:00 - 13:30 lunch
13:30 - 15:30 Free discussion : Lecturers share academic experience with participants and QA in a casual way.
June 10
10:00 - 10:10 opening
10:10 - 11:00 talk 1
11:10 - 12:00 talk 2
12:00 - 13:30 lunch
13:30 - 14:20 Talk 3
14:30 - 15:20 Talk 4
15:30 - 16:00 Coffee Break
16:00 -16:50 Talk 5
June 11
10:10 - 11:00 talk 6
11:10 - 12:00 talk 7
12:00 - 13:30 lunch
13:30 - 14:20 Talk 8
14:30 - 15:20 Talk 9
15:30 - 16:00 Coffee Break
16:00 -16:50 Talk 10
Join us online: https://ntucc.webex.com/ntucc-en/j.php?MTID=m87d629bc6de5299e999c4a57fc506849
National Center for Theoretical Sciences (Math Division),
Chee-Chun Leung Cosmology Hall, No. 1, Sec. 4, Roosevelt Rd., Taipei City 106, Taiwan.
臺北市羅斯福路四段1號臺灣大學梁次震宇宙館
Dinning Map near NCTS (by Peggy) :