Publications & Preprints

21. Quantitative pointwise estimates of the cooling process for inelastic Boltzmann equation, with Gayoung An and Donghyun Lee, arXiv:2406.15077 [math.AP]

20. Measure-valued solution to the inelastic Boltzmann equation for hard potentials without angular cutoff, with Kunlun Qi, AIP Conf. Proc. 2996, 040008 (2024).

19. Compactness and existence theory for a general class of stationary radiative transfer equations, with Elena Demattè and Juan J. L. Velázquez, arXiv:2401.12828 [math.AP]

18. On the temperature distribution of a body heated by radiation, with Juan J. L. Velázquez, SIAM J. Math. Anal. 56(3) (2024), pp. 3478-3508. arXiv:2211.11289 [math.AP]

17. Vanishing angular singularity limit to the hard-sphere Boltzmann equation, with Bernhard Kepka, Alessia Nota, Juan J. L. Velázquez, J. Stat. Phys. 190 (2023), Paper No. 77, 14 pp. arXiv:2209.14075 [math.AP]

16. Global existence and moment creation for the inelastic Boltzmann equation for hard potentials without angular cutoff, with Kunlun Qi, arXiv:2206.09636 [math.AP]  

15. Magnetic confinement for the 2D axisymmetric relativistic Vlasov-Maxwell system in an annulus, with Robert M. Strain and Tak Kwong Wong, Kinet. Relat. Models.,15 (2022), no. 4, 569-604. arXiv:2111.04583 [math.AP]

14. LTE and Non-LTE Solutions in Gases Interacting with Radiation, with Juan J. L. Velázquez, J. Stat. Phys., 186 (2022), no. 3, Paper No. 47, 62 pp. arXiv:2109.10071 [math.AP]

13. Asymptotic Stability of the Relativistic Boltzmann Equation without Angular Cut-off, with Robert M. Strain, Ann. PDE, 8 (2022), no. 2, Paper No. 20, 167 pp. arXiv:1601.02704, arXiv:2102.08846, and arXiv:2103.15885 [math.AP] 

12. Sobolev Training for Physics Informed Neural Networks, with Hwijae Son, Woo Jin Han, and Hyung Ju Hwang, Commun. Math. Sci., 21 (2023), No. 6, pp. 1679-1705. arXiv:2101.08932 [math.NA]

11. The relativistic quantum Boltzmann equation near equilibrium, with Gi-Chan Bae and Seok-Bae Yun, Arch. Ration. Mech. Anal., 240 (2021), no. 3,1593-1644. arXiv:2012.14213 [math.AP]

10. Kinetic Models for Semiflexible Polymers in a Half-plane, with Juan J. L. Velázquez, Pure Appl. Anal. 5 (2023), no. 1, 145-212. arXiv:2011.01491 [math.AP]

9. The model reduction of the Vlasov-Poisson-Fokker-Planck system to the Poisson-Nernst-Planck system via the Deep Neural Network Approach, with Jae Yong Lee and Hyung Ju Hwang, ESAIM Math. Model. Numer. Anal., 55 (2021), no. 5, 1803-1846. arXiv:2009.13280 [math.NA]

8. Compactness properties and local existence of weak solutions to the Landau equation, with Hyung Ju Hwang, Proc. Amer. Math. Soc., 148 (2020), no.12, 5141-5157.

7. Averaging with a time-dependent perturbation parameter, with David Fajman and Gernot Heißel, Classical Quantum Gravity, 38 (2021), no. 8, Paper No. 085005, 12 pp. arXiv:2006.12844 [math.DS]

6. On the Determinant Problem for the Relativistic Boltzmann Equation, with James Chapman and Robert M. Strain, Comm. Math. Phys., 384 (2021), no. 3, 1913-1943. arXiv:2006.02540 [math.AP]

5. Propagation of L^p estimates for the Spatially Homogeneous Relativistic Boltzmann Equation, with Seok-Bae Yun, J. Differential Equations, 272 (2021), 105-126.  arXiv:2001.11672 [math.AP]

4. Trend to Equilibrium for the Kinetic Fokker-Planck Equation via the Neural Network Approach, with Hyung Ju Hwang, Hyeontae Jo, and Jae Yong Lee, J. Comput. Phys., 419 (2020), 109665, 25 pp. arXiv:1911.09843 [math.NA]

3. Propagation of uniform upper bounds for the spatially homogeneous relativistic Boltzmann equation, with Robert M. Strain and Seok-Bae Yun, Arch. Ration. Mech. Anal., 241 (2021), no. 1, 149-186. arXiv:1907.05784 [math.AP]

2. The Landau equation with the specular reflection boundary condition, with Yan Guo, Hyung Ju Hwang, and Zhimeng Ouyang, Arch. Ration. Mech. Anal., 236 (2020), no. 3, 1389-1454. arXiv:1905.00173 and arXiv:2009.01391 [math.AP]

1. Gain of regularity for the relativistic collision operator, with Seok-Bae Yun, Appl. Math. Lett., 90 (2019), 162-169. arXiv:1808.10147 [math.AP]

Ph.D. Thesis

Global classical solutions to the relativistic Boltzmann equation without angular cut-off. Thesis (Ph. D.)-University of Pennsylvania, 2016. 135 pp. ISBN: 978-1339-92867-8,  ProQuest LLC - awarded The Carlitz-Zippin Prize (2016).

Undergraduate Research (NSF-REU)

Fixed Point Floer Homology via the Hochschild Homology of a Sequence of Curves, with Rachel Vishnepolsky and Xuran Wang, Rose-Hulman Undergraduate Mathematics Journal,  11 (2010), no. 2, Art. 9, 20 pp.