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
Supersonic flows of the Euler-Poisson system in three-dimensional cylinders (with H. Park), J. London Math. Soc. (2) (2025)
Prandtl-Meyer Reflection Configurations, Transonic Shocks, and Free Boundary Problems (with G.-Q. Chen and M. Feldman) , Memoirs of the AMS (2024), Volume 301, Number 1507
A Review on Two Types of Sonic Interfaces, Commun. Math. Anal. Appl., 3 (2024), pp. 384-401.
Detached shock past a blunt body (with W. Xiang), Acta Appl Math 188, 7 (2023).
Three dimensional supersonic flows of Euler-Poisson system for potential flow (with H. Park), Communications on Pure & Applied Analysis (published online) (2021)
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).
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
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
Contact discontinuities for 3-D axisymmetric inviscid compressible flows in infinitely long cylinders (with H. Park) , J. Differential Equations, 267(2019) 2824-2873
Contact discontinuities for 2-D inviscid compressible flows in infinitely long nozzles (with H. Park), SIMA , 51 no.3 (2019) 1730-1760
Radial transonic shock solutions of Euler-Poisson system in convergent nozzles (with Y. Park), DCDS-S, 11 no.5(2018) 773-791
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
Subsonic flow for multidimensional Euler-Poisson system
(with B. Duan and C. Xie) Arch. Rational Mech. Anal. 220 (2016) 155–191
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
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
Stability of contact discontinuity for steady Euler system in infinite duct
Z. Angew. Math. Phys. 64 (2013) pp 917–936
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
Transonic Shocks in Multi-dimensional Divergent Nozzles
(with M. Feldman) Arch. Rat. Mech. Anal., 201(2011), no 3, pp. 777–840
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
Preprints (Mostly available on ArXiv.org)
Global Uniqueness of Subsonic Flows for the Steady Euler-Poisson System (with B. Duan, M. Jo and C. Xie)
Contact Discontinuities for 3-D Axisymmetric Flows with Non-Zero Swirl (with J. Yoon), submitted
Recent Developments on Transonic Shocks Past Two-Dimensional Curved-Nose Bodies (with Y. Pei and W. Xiang), submitted
Existence of strong transonic shock solutions of steady Euler flow past a wedge (with J. Liao), to appear on J. London Math. Soc.
Classical solutions to a mixed-type PDE with a Keldysh-type degeneracy and accelerating transonic solutions to the Euler-Poisson system (with B. Duan and C. Xie), submitted (This result is a generalization of "The steady Euler-Poisson system and accelerating flows with transonic C^1-transitions")
The steady Euler-Poisson system and accelerating flows with transonic C^1-transitions (with B. Duan and C. Xie), arXiv:2308.04694
(Former) Graduate students
Jongseo Yun(Current, PhD program, KAIST)
Minsuh Jo (Current, PhD program, KAIST)
Haneul Kang (Current, PhD program, KAIST)
Dae Young Jeong (Graduated in 2025 , MA, KAIST)
Hyun Jun Kim (Graduated in 2024, MA, KAIST)
Jung Wook Chun (Graduated in 2025, MA, KAIST)
Minjung Kim (graduated in 2023, MA, KAIST)
Hyangdong Park (2019, Former PhD student at POSTECH)
Hyeongyu Ryu (2020, Former PhD student at POSTECH)
Yong Park(2019, Former PhD student at POSTECH)
Heonjin Ha (2019, Former Master student at POSTECH)
(Former) Postdocs
Hyangdong Park (Current, Postdoc, KAIST)
Pei Yu (Former Postdoc at KAIST, currently a postdoc at Hong Kong Polytech)
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…
check my publications and see if they match your research interest;
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.