H.Yuan

Hairong Yuan （袁海荣）

Professor

School of Mathematical Sciences

East China Normal University

Dongchuan Rd. 500, Minhang, Shanghai 200241

Email: hryuan@math.ecnu.edu.cn

Office: Math. Building, Room S329

Ph.D. Fudan University, 2006

My Curriculum Vitae （English version）(not updated)

我的简历（中文版）(updated)

Introduction

I am a professor of applied mathematics at the School of Mathematical Sciences, East China Normal University at Shanghai, China. I got Bachelor of Science from Fudan University in 2001, and Ph.D.in 2006, also from Fudan University, under the guidance of Professor Shuxing Chen. Then I worked at East China Normal University, as Postdoc, Lecturer, Associate Professor and full Professor. I visited Prof. Gui-Qiang Chen at University of Oxford, UK from March 2011 to Feb. 2012, supported by China Scholarship Council.

All my research work is devoted to the compressible Euler equations and related problems in mathematical gas dynamics. My studies cover subsonic flows, transonic flows, supersonic flows and hypersonic flows. The Euler equations behave quite differently in these cases, so mathematically my research involves hyperbolic systems of conservation laws, first-order and second-order elliptic equations, elliptic-hyperbolic mixed type equations, first-order elliptic-hyperbolic composite systems. I studied piecewise smooth solutions, integral weak solutions and Radon measure solutions of Euler equations. Besides partial and ordinary differential equations, functional analysis, my research work also need tools from differential geometry, measure theory and Fourier analysis.

Up to now, there are four parts of my research: (1) Free boundary problems of Euler equations and stability of transonic shock in ducts; (2) Radon measure solutions of Euler equations and mathematical theory of Newton-Busemann pressure law in hypersonic flows; (3) Initial-boundary value problems of multidimensional hyperbolic systems; (4) BV weak solutions of supersonic jet flows.

Teaching

以下备课讲义可供选课同学下载使用：

※ “《海洋科学的数学原理》夏令营”部分讲义（流体力学方程建模、变分原理）（本科生、研究生， 2024年8月）

※《随机微分方程基本理论及应用》（刘见礼、袁海荣编著，科学出版社，2024年6月）

※ 《Brown 运动、Wiener 测度、路径积分、Feynman-Kac 公式和随机积分的数学理论导引》（本科生、研究生，2023年2月）

※ 《偏微分方程》（本科生，2023年1月）

※ 《连续方程与曲线空间上的概率测度》（研究生，2021年10月）

※ 《双曲型偏微分方程讲义——高维双曲型方程组的初边值问题数学理论导引》（研究生，2021年6月）

※《双曲守恒律方程与激波数学理论导引》（研究生，目前只包括三章，2020年12月）

※ 《微分几何讲义》（适用于本科生的《微分几何》课程，2014年10月，部分完成）

※《点集拓扑学讲义》（适用于本科生的《点集拓扑学》课程，2014年6月，2019年7月）

※《调和分析与偏微分方程讲义》（适用于研究生，2013年4月，2021年6月）

※《线性代数讲义》（入门课程，适用于低年级本科生, 2009年12月）

For more information on courses I have taught, click here: Teaching (mainly in Chinese)

Mathematical Research Interests Preprints and Publications

Presently my research work involves:

• Partial Differential Equations

- of elliptic, hyperbolic, elliptic-hyperbolic composite-mixed type； free boundary problems

-hyperbolic systems of conservation laws

• Mathematical Problems in Fluid Dynamics

- Compressible Euler equations； subsonic flows；transonic shocks and transonic flows； supersonic flows and hypersonic flows

• Fluid Flows in Curved Spaces

• Measure-valued solutions of PDE and their applications

学术报告的PPT

※《高超音极限流与可压缩 Euler方程组的Radon测度解——锥体绕流Newton-Busemann压强律的数学证明及其推广》（2020年12月）

※《管道内高维定常可压欧拉流中跨音激波的稳定性问题——几何、摩擦和热交换效应》（2020年12月）

Acknowledgements

Without help of the community, a single person can achieve nothing today. My research was kindly supported by many foundations or grants listed in my CV. I also thank sincerely my institute, teachers, colleagues, family, as well as the referees for their constant supports and encouragements!

Go back to Department of Mathematics, ECNU or visit Fudan University, School of Mathematical Sciences