Donghyun Lee

CV

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Research Interests

Applied PDE, Fluid mechanics, Kinetic theory

Publication & Preprint

A Physics-Informed, Global-in-Time Neural Particle Method for the Spatially Homogeneous Landau Equation (M. Kim,  S. Son, Y. Kim, and D. Lee) (2026) preprint, arXiv

Global Solutions in $L^p_{v} L^\infty_{x}$ for the Boltzmann Equation in Bounded Domains (D. Deng, J. Kim and D. Lee) (2025) preprint, arXiv

Optimal C^1/2 regularity of the Boltzmann equation in non-convex domains (G. An and D. Lee) (2025) in revision, arXiv

On the large amplitude solution of the Boltzmann equation with large external potential and boundary effects (J. Kim and D. Lee) J. Stat. Phys., Vol 192, No 77, (2025) link, arXiv

Ill-posedness of the Boltzmann-BGK model in the exponential class (D. Lee, S. Park and S. Yun) (2024) accepted in Arch. Rational Mech. Anal., arXiv

Quantitative pointwise estimates of the Cooling process for inelastic Boltzmann equation (G. An, J. Jang and D. Lee) J. Stat. Phys., Vol 192, No 112, (2025) link, arXiv

[Proceedings] H\"older regularity of the Boltzmann equation in some non-convex domains (C. Kim and D. Lee) AIP Conf. Proc. 2996, 040007 (2024) link

The Mixed Convex-Concave effect on the regularity of a Boltzmann solution (G. An and D. Lee) SIAM J. Math. Anal., Vol 57, Issue. 1, (2025) link, arXiv

Dynamical billiard and a long-time behavior of the Boltzmann equation in general 3D toroidal domains (G. Ko, C. Kim and  D. Lee) Tunis. J. Math., Vol 7, No 2, pp. 229-338 (2025) link, arXiv

Large amplitude problem of BGK model : Relaxation to quadratic nonlinearity (G. Bae, G. Ko,  D. Lee and S. Yun) (2023) accepted in SIAM J. Math. Anal., arXiv

High-velocity tails of the inelastic and the multi-species mixture Boltzmann equations (G. An and D. Lee) SIAM J. Math. Anal., Vol 55, No. 5, pp. 4297-4336 (2023) link, arXiv

On  C^2 solution of the free transport equation in a disk (G. Ko and  D. Lee) Kinet. Relat. Models., Vol 16, No. 3, pp 311-372 (2023), link, arXiv

H\"older regularity of the Boltzmann equation past an obstacle (C. Kim and D. Lee) Comm. Pure Appl. Math, Vol 77, Issue4, pp 2331-2386 (2024), link, arXiv

The large amplitude solution of the Boltzmann equation with soft potential (G. Ko, D. Lee and G. Park) J. Differ. Equ, Vol 307 (2022), pp. 297-347 link, arXiv

The Boltzmann equation with large-amplitude initial data and specular reflection boundary condition (R. Duan, G. Ko and D. Lee) J. Stat. Phys., Vol 190, No. 189 (2023) link, arXiv

Global strong solutions of the Vlasov-Poisson-Boltzmann system in bounded domains (Y. Cao, C. Kim and D. Lee) Arch. Rational Mech. Anal., 233(3), pp. 1027-1130 (2019) link, arXiv

Decay of the Boltzmann equation with the specular boundary condition in non-convex cylindrical domains (C. Kim and D. Lee) Arch. Rational Mech. Anal., 230(1), pp. 49-123 (2018) link, arXiv

The Boltzmann equation with specular boundary condition in convex domains (C. Kim and D. Lee) Comm. Pure Appl. Math., 71 (2018), pp.411-504. link, arXiv

Uniform estimate of viscous free-boundary magnetohydrodynamics with zero vacuum magnetic field (D. Lee) SIAM J. Math. Anal., 49-4 (2017), pp. 2710-2789. link, arXiv

Initial value problem for the free boundary magnetohydrodynamics with zero magnetic boundary condition (D. Lee) Comm. Math. Sci., Vol 16, No. 3, pp 589-615 (2018). link, arXiv

Uniform Regularity for Free boundary Navier-Stokes Equations with Surface tension (T. Elgindi and D. Lee) J. Hyperbol. Differ. Eq., Vol. 15, No. 01, pp. 37-118 (2018). link, arXiv

Link

Department of Mathematics, POSTECH

PDE and Applied Analysis Seminar (PDEAA)

CM2LA (SRC)

Korea-France Webinar (Kinetic and Fluid equations for Collective Dynamics)