Hairong Yuan   (袁海荣)

Professor

Department of Mathematics

East China Normal University

Dongchuan Rd.  500,  Minhang,  Shanghai 200241

Email:  hryuan@math.ecnu.edu.cn

Office:   Math. Building,  Room 114 

Ph.D.  Fudan University, 2006                       

My Curriculum Vitae English version                          我的简历(中文版)

Introduction

I am a professor of 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. Then I worked at East China Normal University, as Postdoc, Lecturer, Associate Professor and full Professor.

All of my research works are 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 for 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 Some Slides and Lecture Notes, mainly in Chinese

以下备课讲义可供选课同学下载使用:

【本科生】

2014年春季学期:《点集拓扑学讲义》(适用于本科生的《点集拓扑学》课程,20146月;20196月修改)

2014年秋季学期:《微分几何讲义》(适用于本科生的《微分几何》课程,201410月,部分完成)

《线性代数讲义》(入门课程,适用于低年级本科生及继续教育学院学员,200912月)

【研究生】

《调和分析与偏微分方程讲义》适用于研究生,20134月;20216月修改)

双曲型偏微分方程讲义——高维双曲型方程组初边值问题数学理论导引(适用于研究生,20216月)

※《双曲守恒律方程与激波数学理论导引》(目前只包括三章,202012月)

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》202012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》202012月)

 

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


Mathematical Research Interests  

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 flowstransonic shocks and  transonic flows supersonic flows and hypersonic flows

Fluid Flows in Curved Spaces  



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 

Last updated by H. Yuan:  June. 15, 2021        2006-2021 @ All rights reserved!