Kinetic equations
Boltzmann equation
BGK and ES-BGK models
Landau equation
Mathematical analysis of kinetic models
Scientific machine learning
Physics-informed neural networks
Neural particle methods
Local in Time Solution for the ES-BGK Model with Correct Prandtl Number Sung-Jun Son and Seok-Bae Yun. Kinetic and Related Models, 18(4), 499–519, 2025.
Global Stability of the Boltzmann Equation for a Polyatomic Gas with Initial Data Allowing Large Oscillations Gyounghun Ko and Sung-Jun Son. Journal of Differential Equations, 425, 506–552, 2025.
(L^p)-Solutions to the ES-BGK Model of the Polyatomic Molecules Sung-Jun Son. Journal of Mathematical Physics, 65, 101501, 2024.
The ES-BGK for the Polyatomic Molecules with Infinite Energy Sung-Jun Son and Seok-Bae Yun. Journal of Statistical Physics, 190, 129, 2023.
Cauchy Problem for the ES-BGK Model with Correct Prandtl Number Sung-Jun Son and Seok-Bae Yun Partial Differential Equations and Applications, 3, 41, 2022.
Convergence of Alternating Score–System Iterations for Regularized Landau Particle Dynamics with Yeoneung Kim, and Donghyun Lee. Submitted.
Exponential Ill-posedness of the BGK Model in a Half-Space with Inflow Boundary Conditions with Donghyun Lee, Sungbin Park, and Seok-Bae Yun. Submitted.
A Physics-Informed Neural Particle Method for the Spatially Homogeneous Landau Equation with Minseok Kim, Yeoneung Kim, Donghyun Lee, and Sung-Jun Son. Submitted.
A Theory-Grounded Weighted (L^2)-Norm for Solving the BGK Model via Physics-Informed Neural Networks with Gyounghun Ko, Seung-Yeon Cho, Myeong-Su Lee, and Sung-Jun Son. Submitted.
Global Well-Posedness for the Multi-Species Boltzmann Equation with Large Amplitude Initial Data with Gyounghun Ko, Myeong-Su Lee, and Sung-Jun Son. Submitted.
I study analytical problems arising in kinetic equations, with particular interests in well-posedness, stability, large-amplitude solutions, and boundary problems for the Boltzmann and BGK equations.
Current projects include:
Global weighted (L^p)-solutions to a BGK model for binary gas mixtures with density-ratio collision frequencies
Joint particle, Fourier, and iteration limits for score-based Vlasov–Maxwell–Landau dynamics with Yeoneung Kim, and Donghyun Lee.
I am also interested in developing machine-learning-based numerical methods that incorporate the underlying mathematical and physical structures of kinetic equations.
Current projects include:
Transport-aware neural sampling for a regularized BGK particle process: accuracy and structural limitations with Minseok Kim, Yeoneung Kim, and Donghyun Lee.
Why Conservation Constraints Improve PINNs for Linearized Kinetic Equations with Gyounghun Ko, Seung-Yeon Cho, Myeong-Su Lee, and Sung-Jun Son
A Physics-Informed Neural Particle Method for the Vlasov–Maxwell–Landau Equation with Minseok Kim, Yeoneung Kim, and Donghyun Lee.
Approximation of High-Dimensional Kinetic Dynamics via Neural Networks in Score-Based Particle Methods Principal Investigator (PI)
Basic Science Research Program, National Research Foundation of Korea (NRF), funded by the Ministry of Education Grant No. RS-2025-25419038 (September 2025 – August 2028)