Research

My research interest lies on analysis of nonlinear partial differential equations. Currently, I am working on free boundary problem with nonlinear mixed-type PDEs arising from fluid mechanics. In particular, my recent research is focused on smooth/non-smooth transonic flows of Euler system/Euler-Poisson system.

Papers

Published

1.  Detached shock past a blunt body (with W. Xiang), Acta Appl. Math. (published online) (2023)

2.  Three dimensional supersonic flows of Euler-Poisson system for potential flow (with H. Park), Communications on Pure & Applied Analysis (published online) (2021)

3.  Structural stability of Supersonic solutions to the Euler-Poisson system (with B. Duan, J.-J. Xiao and C. Xie), Arch. Rat. Mech. Anal.  239, 679–731 (2021). 

4. A summary on the existence theorem of detached shock solutions of potential flow and a discussion about detached shock solutions of full Euler system (with. W. Xiang) ,  RIMS Kôkyûroku (2020) No.2155

5. A note on 2-d detached shocks of steady Euler system (with W. Xiang),  Proceedings of the HYP2018 conference, AIMS on Applied Mathematics Vol. 10 (2020) 124-135

6. Contact discontinuities for 3-D axisymmetric inviscid compressible flows in infinitely long cylinders (with H. Park) , J. Differential Equations, 267(2019) 2824-2873

7. Contact discontinuities for 2-D inviscid compressible flows in infinitely long nozzles (with H. Park), SIMA , 51 no.3 (2019) 1730-1760

8. Radial transonic shock solutions of Euler-Poisson system in convergent nozzles (with Y. Park),  DCDS-S,  11 no.5(2018) 773-791

9. 3-D axisymmetric subsonic flows with nonzero swirl for the compressible Euler-Poisson system (with S. Weng), ANN. I. H. Poincarè-AN, 35 no.1 (2018) 161-186  

10. Subsonic flow for multidimensional Euler-Poisson system
    (with B. Duan and C. Xie) Arch. Rational Mech. Anal. 220 (2016) 155–191

11. Two dimensional subsonic flows with self-gravitation in bounded domain (with B. Duan and C. Xie) Math. Models Methods Appl. Sci. Vol. 25, No. 14 (2015) 2721–2747

12. Subsonic solutions for steady Euler-Poisson system in two dimensional nozzles (with B. Duan and C. Xie) SIAM J. Math. Anal.(2014),  46(5), 3455–3480　

13. Stability of contact discontinuity for steady Euler system in infinite duct
    Z. Angew. Math. Phys. 64 (2013) pp 917–936  

14. Prandtl-Meyer reflection for supersonic flow past a solid ramp
    (with G.-Q. Chen and M. Feldman), Quart. Appl. Math. (2013) no 3, pp 583–600　

15. Transonic Shocks in Multi-dimensional Divergent Nozzles
    (with M. Feldman) Arch. Rat. Mech. Anal., 201(2011), no 3, pp. 777–840

16. Regularity of Solutions to Regular Shock Reflection for Potential Flow
    (with G.-Q. Chen and M. Feldman) Invent. Math. 175(2009) no 3, pp. 505-543
    
    　

Submitted Preprints  (Mostly available on ArXiv.org)

1. Prandtl-Meyer Reflection Configurations, Transonic Shocks, and Free Boundary Problems (with G.-Q. Chen and M. Feldman) , To appear in Memoirs of the AMS ,  arXiv:1901.05916 

2. Supersonic flows of the Euler-Poisson system in three-dimensional cylinders (with H. Park), submitted, arXiv:2302.03308v2 

3. The steady Euler-Poisson system and accelerating flows with transonic C^1-transitions (with B. Duan and C. Xie), submitted, arXiv:2308.04694 

4.  A review on two types of sonic interfaces, submitted

In preparation

1. Transonic shock solutions of Euler-Poisson system  (with B. Duan and C. Xie)

2. The steady Euler-Poisson system and 3-D accelerating flows with transonic C^1-transitions (with H. Park)

3. Detached shock past a blunt body for steady full Euler system (with W. Xiang and P. Yu)

(Former) Graduate students

• Minseo Jo (Current, PhD program, KAIST)

• Sumin Kang (Current, PhD program, KAIST)

• Dae Young Jeong (Current, PhD program, KAIST)

• Hyun Jun Kim (Current, Master program, KAIST)

• Jung Wook Chun (Current, Master program, KAIST)

• Minjung Kim (graduated in 2023, MA,  KAIST, )

• Hyangdong Park (2019, Former PhD student at POSTECH, Current position: Postdoc researcher at CMAC, Yonsei University)

• Hyeongyu Ryu (2020, Former PhD student at POSTECH)

• Yong Park(2019, Former PhD student at POSTECH, Current position: Wu Wen-Tsun Assistant professor, Shanghai Jiao Tong University, China)

• Heonjin Ha (2019, Former Master student at POSTECH)

(Former) Postdocs

• Pei Yu (Current, Postdoc, KAIST)

• Shangkun Weng (Former research assistant professor of PMI at POSTECH, currently a professor at Wuhan University, China)

• Ben Duan  (Former research assistant professor of PMI at POSTECH, currently a professor at Jilin University, China)

Are you interested to join my lab? Then, you should…

1. check my publications and see if they match your research interest;

2. check if you took, or are taking the following graduate courses : Graduate analysis courses (real analysis required, functional analysis, complex analysis recommended) & Graduate level PDE course.