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.
　

  • Nonlinear PDEs
  • Free boundary problems
  • Mathematical fluid dynamics

Papers

Published

  1. Structural stability of Supersonic solutions to the Euler-Poisson system (with B. Duan, J.-J. Xiao and C. Xie), publihsed online in Arch. Rat. Mech. Anal. (2020), arXiv:1602.01892 
  2. 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
  3. Contact discontinuities for 3-D axisymmetric inviscid compressible flows in infinitely long cylinders (with H. Park) , J. Differential Equations, 267(2019) 2824-2873
  4. Contact discontinuities for 2-D inviscid compressible flows in infinitely long nozzles (with H. Park), SIMA , 51 no.3 (2019) 1730-1760
  5. Radial transonic shock solutions of Euler-Poisson system in convergent nozzles (with Y. Park),  DCDS-S,  11 no.5(2018) 773-791
  6. 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,  
  7. Subsonic flow for multidimensional Euler-Poisson system
    (with B. Duan and C. Xie) Arch. Rational Mech. Anal. 220 (2016) 155–191
  8. 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
  9. 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　
  10. Stability of contact discontinuity for steady Euler system in infinite duct
    Z. Angew. Math. Phys. 64 (2013) pp 917–936  
  11. 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　
  12. Transonic Shocks in Multi-dimensional Divergent Nozzles
    (with M. Feldman) Arch. Rat. Mech. Anal., 201(2011), no 3, pp. 777–840
  13. 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  (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. Detached shock past a blunt body (with. W. Xiang) , submitted, arXiv:1909.13281

In preparation

  1. 3-D axi-symmetric supersonic solution of Euler-Poisson system (with H. Park)
  2. Transonic shock solutions of Euler-Poisson system (with B. Duan and C. Xie)
  3. Smooth transonic flows of Euler-Poisson system(with B. Duan and C. Xie)

(Former) Graduate students

  • Hyangdong Park , (Former PhD student at POSTECH, Current position: Postdoc researcher at CMAC, Yonsei University)
  • Hyeongyu Ryu, (Current PhD student at POSTECH, PhD thesis defense done on Oct. 23 2020)
  • Yong Park,
    (Former PhD student at POSTECH, Current position: Wu Wen-Tsun Assistant professor, Shanghai Jiao Tong University, China)
  • Heonjin Ha, (Former Master student at POSTECH)

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

(Former) Postdocs

  • Shangkun Weng (Former research assistant professor of PMI, currently a professor at Wuhan University, China)
  • Ben Duan  (Former research assistant professor of PMI, currently a professor at Dalian University of Technology, China)