Workshop on
Viscous Conservation Laws

Introduction

The workshop will be headlined by an introductory mini-course delivered by Professor Akitaka Matsumura. Complementing the mini-course will be talks in order to discuss and disseminate the latest results and trend in the field of nonlinear partial differential equations, particularly in kinetic theory, fluid dynamic equations and chemotaxis models.

Organizing Committee

• Renjun Duan The Chinese University of Hong Kong
• Zhouping Xin The Chinese University of Hong Kong
• Tong Yang City University of Hong Kong

List of Speakers

• Feimin HUANG AMSS, Chinese Academy of Sciences
• Tao LUO City University of Hong Kong
• Akitaka MATSUMURA Osaka University
• Zhian WANG Hong Kong Polytechnic University
• Feng XIE Shanghai Jiao Tong University
• Tong YANG City University of Hong Kong

Program

The workshop will take place at Lady Shaw Building (LSB). The program schedule is shown below.

Title and Abstract

Part 1. Mini-course:

Title:
Some energy methods for viscous conservation laws

Speaker:
Akitaka MATSUMURA
Osaka University

Abstract:
Through some typical Cauchy problems in the field of viscous conservation laws, this short course aims to introduce several elementary energy methods which provide desired "a priori" estimates for the global existence in time and asymptotic behavior of solutions.

Part 2. Talks:

Title:
Isentropic compressible Euler system with source terms

Speaker:
Feimin HUANG
AMSS, Chinese Academy of Sciences

Abstract:
In this talk, we develop a new technique to prove the global existene of entropy solutions to an inhomogeneous isentropic compressible Euler equations through the compensated compactness and vanishing viscosity method.

Title:
Some recent developments of fluids interface problems

Speaker:
Tao LUO
City University of Hong Kong

Abstract:
In this talk, I will survey some recent developments of fluids interface problems.

Title:
System of conservation laws arising from chemotaxis model

Speaker:
Zhian WANG
Hong Kong Polytechnic University

Abstract:
We shall present a system of conservation laws derived from the chemotaxis models describing the initiation of tumor angiogenesis. The system has some exclusive features distinguished itself from the existing systems of conservation, which makes the analysis in multi-dimensional spaces very challenging. In the talks, we shall discuss the system background, the development of mathematical results, interesting open questions and challenges faced.

Title:
Local-in-time well-posedness theory for MHD boundary layer in Sobolev spaces

Speaker:
Feng XIE
Shanghai Jiao Tong University

Abstract:
We study the well-posedness theory for MHD boundary layer. Such a kind of boundary layer equations are governed by the Prandtl type equations, which are derived from MHD with no-slip boundary condition for velocity and perfectly conducting conditions for magnetic fields. Under the assumptions that the initial tangential magnetic is always non-zero, we can establish the local-in-time existence, uniqueness, and stability of solutions for the nonlinear MHD boundary layer equations in weighted Sobolev spaces. This talk is based on the joint work with Dr. Chengjie Liu and Professor Tong Yang from CityU of Hong Kong.

Title:
Measure valued solutions to the Boltzmann equation

Speaker:
Tong YANG
City University of Hong Kong

Abstract:
In this talk, we will present some recent results on the well-posedness, regularity and large time behavior of the measure valued solutions. The results are from several joint works with Yong-Kum Cho,Yoshinori Morimoto, Shuaikun Wang and Huijiang Zhao.

Maps & Directions

The workshop sessions will be held in the Lady Shaw Building (LSB).

Please follow the instruction below if you are going from the University MTR Station:

Take Shuttle Bus 1A / 1B / H near MTR Exit A - C or Shuttle Bus 3 near MTR Exit D. Get off at the second stop (Sir Run Run Shaw Hall).

(Shuttle Bus Route Information / Shuttle Bus Timetable)

The rooftop garden opposite Sir Run Run Shaw Hall is part of Lady Shaw Building. Go there and enter the lift on the right under the flat canopy. It is a three-minute walk. The seminar rooms 219 and 222 are on 2/F.

Sponsors

The workshop is generously supported by the following organizations:

Department of Mathematics,
The Chinese University of Hong Kong

Institute of Mathematical Sciences,
The Chinese University of Hong Kong