I am a postdoctoral researcher at IRMAR, Univ. of Rennes, France.
My research interests lie in the area of partial differential equations. I am particularly interested in a variety of phenomena arising in PDEs governing behaviors of plasmas. These include
stability of nonlinear waves,
similarities between plasma waves and water waves,
relations between fluid models and kinetic models of plasmas.
Email : junsik.bae@univ-rennes.fr; altena00@gmail.com (personal email)
(with W. Choi and Y.-J. Kim) Quadratic Growth Model with Discontinuity: A Link between Monostable and Bistable Traveling Waves, preprint arXiv
(with Y. Kim and B. Kwon) Structure of singularities for the Euler-Poisson system of ion dynamics, preprint arXiv
(with Y. Kim and B. Kwon) Delta-shock for the pressureless Euler-Poisson system, SIAM J. Math. Anal, 57 (3) (2025) 3255-3296 arXiv
(with S.H. Moon and K. Woo) Emergence of peaked singularities in the Euler-Poisson system, J. Nonlinear Sci. 35, 25 (2025) (SharedIt) arXiv
(with J. Choi and B. Kwon) Singularity formation of hydromagnetic waves in cold plasma, Appl. Math. Lett. 160 109344 (2025) (Share Link) arXiv
(with D. Kawagoe) Nonexistence of multi-dimensional solitary waves for the Euler-Poisson system, Physica D 470 134347 (2024) arXiv
(with J. Choi and B. Kwon) Formation of singularities in plasma ion dynamics, Nonlinearity 37 045011 (2024) arXiv
(with B. Kwon) Linear Stability of Solitary Waves for the Isothermal Euler-Poisson system, Arch Ration Mech Anal 243, 257-327 (2022) (SharedIt link) arXiv
(with B. Kwon) Small amplitude limit of solitary waves for the Euler-Poisson system, J. Differential Equations 266 (2019) 3450-3478 arXiv
(with B. Kwon and S. Moon) Reconstruction of the initial state from the data measured on a sphere for plasma-acoustic wave equations, Inverse Problems 34 (2018) 105004
Workshops and Seminars
Lecture series on dynamical systems (2025.06.16.~2025.06.18)
Lecture series on computer-assisted proofs in nonlinear analysis (2024.10.29.~2024.11.01)
The 5th Workshop on recent development of mathematical fluid dynamics and hyperbolic conservation laws (2023.08.31 ~ 09.03)
UNIST Mini-Workshop on Differential Equations (2023.04.11)
Talk slide (Informal talk at NTU) - Solitary waves of the Euler-Poisson system. We introduce the small-amplitude limit of solitary waves for the 1D Euler-Poisson system with the Boltzmann relation. Also, we introduce the linear stability of small amplitude solitary waves for the isothermal system. We use the Evans function to study the associated eigenvalue problem. It is discussed why the energy method is inappropriate in our situation.
Talk slide (2020 NCTS PDE Young Scholar Workshop) - Solitary waves for the Euler-Poisson system and numerical observations. A linear instability criterion for large amplitude solitary waves of the 1D isothermal Euler-Poisson system is discussed. Some numerical observations are presented, which lead to the question of global existence vs. finite time blow-up for the 1D pressureless Euler-Poisson system.
Talk slide (2021 NCTS Spring day) - Formation of singularities in cold ion dynamics and some numerical observations. We show that the 1D pressureless Euler-Poisson system with the Boltzmann relation blows up in a finite time even if the initial velocity gradient is identically zero. We discovered some interesting properties of the system and a certain second-order differential inequality.
Talk Slide (Ignite Talks, 2021, NCTS) - KdV history. Each speaker prepared 20 slides, which automatically advance every 15 seconds. I prepared a brief history of the KdV equation and some stories.