Publication

Preprints

36. On the partial semi-classical Weyl's law (with Sangdon Jin), Preprint

35. Global well-posedness of the nonlinear Hartree equation for infinitely many particles with singular interaction (with Sonae Hadama), Preprint

34. Semi-classical equivalence of two white dwarf models as ground states of the relativistic Hartree-Fock and Vlasov-Poisson energies  (with Sangdon Jin and Jinmyoung Seok), Preprint

33. Global existence versus finite time blowup dichotomy for the dispersion managed NLS (with Mi-Ran Choi and Young-Ran Lee), Preprint

32. On steady states for the Vlasov-Schrödinger-Poisson system (with Sangdon Jin), Preprint

31. On the NLS approximation for the nonlinear Klein-Gordon equation (with Seokchang Hong), Preprint

30. On the Korteweg-de Vries limit for the Boussinesq equation  (with Changhun Yang), to appear in J. Differential Equations

Published Articles

29. Uniqueness and orbital stability of standing waves for the nonlinear Schrödinger equation with a partial confinement (with Sangdon Jin), SIAM J. Math. Anal. 56 (2024), no. 2, 2714–2737.

28. On the nonlinear Schrödinger equation with a toroidal-shaped trap in the strong confinement regime (with Sangdon Jin), Nonlinearity 36 (2023), no. 5, 2741–2791.

27. On the continuum limit for the discrete nonlinear Schrödinger equation on a large finite cubic lattice (with Chulkwang Kwak and Changhun Yang), Nonlinear Anal. 227 (2023), Paper No. 113171, 26 pp.

26. Orbital stability for the mass-critical and supercritical pseudo-relativistic nonlinear Schrödinger equation (with Sangdon Jin), Discrete Contin. Dyn. Syst. 42 (2022), no. 7, 3103–3118.

25. Strichartz estimates for higher-order Schrödinger equations and their applications (with Chulkwang Kwak and Changhun Yang),  J. Differential Equations 324 (2022), 41–75.

24. Ground states to the generalized nonlinear Schrödinger equations with Bernstein symbols (with Jinmyoung Seok), Anal. Theory Appl. 37 (2021), no. 2, 157–177 (Dedicated to Prof. Paul H. Rabinowitz with admiration on the occasion of his 80th birthday) 

23. On the Korteweg-de Vries limit for the Fermi-Pasta-Ulam system (with Chulkwang Kwak and Changhun Yang), Arch. Ration. Mech. Anal. 240 (2021), no. 2, 1091–1145.

22. Finite difference scheme for two-dimensional periodic nonlinear Schrödinger equations (with Chulkwang Kwak, Shohei Nakamura, Changhun Yang), J. Evol. Equ. 21 (2021), no. 1, 391–418.

21. Semi-classical limit of quantum free energy minimizers for the gravitational Hartree equation (with Woocheol Choi and Jinmyoung Seok), Arch. Ration. Mech. Anal. 239 (2021), no. 2, 783–829

20. On critical and super-critical pseudo-relativistic nonlinear Schrödinger equations (with Woocheol Choi and Jinmyoung Seok),  Proc. Roy. Soc. Edinburgh Sect. A 150 (2020), no. 3, 1241–1263. 35 

19. On the Strichartz estimates for orthonormal systems of initial data with regularity (with Neal Bez, Sanghyuk Lee, Shohei Nakamura, Yoshihiro Sawano), Adv. Math. 354 (2019), 106736, 37 pp.

18. Convergence rate of the finite element approximation for extremizers of Sobolev inequalities (with Woocheol Choi and Jinmyoung Seok), Calcolo 56 (2019), no. 3, Art. 27, 21 pp. 

17. Uniform Strichartz estimates on the lattice (with Changhun Yang), Discrete Contin. Dyn. Syst. 39 (2019), no. 6, 3239-3264.

16. Global existence versus finite time blowup dichotomy for the system of nonlinear Schrödinger equations (with Soonsik Kwon and Haewon Yoon), J. Math. Pures Appl. (9) 125 (2019), 283–320.

15. Strong convergence for discrete nonlinear Schrödinger equations in the continuum limit (with Changhun Yang), SIAM J. Math. Anal. 51 (2019), no. 2, 1297–1320.

14. Semilinear elliptic equations with the pseudo-relativistic operator on a bounded domain (with Woocheol Choi and Jinmyoung Seok), Nonlinear Anal.  173  (2018), 123–145.

13. Uniqueness and symmetry of ground states for higher-order equations (with Woocheol Choi and Jinmyoung Seok), Calc. Var. Partial Differential Equations  57  (2018),  no. 3, 57:77.

12. On the scattering problem for infinitely many fermions in dimensions d ≥ 3 at positive temperature (with Thomas Chen and Nataša Pavlović), Ann. Inst. H. Poincaré Anal. Non Linéaire  35  (2018),  no. 2, 393–416.

11. Optimal convergence rate of nonrelativistic limit for the nonlinear pseudo-relativistic equations (with Woocheol Choi and Jinmyoung Seok), J. Funct. Anal.  274  (2018),  no. 3, 695–722.

10. Strichartz estimates for N-body Schrödinger operators with small potential interactions, Discrete Contin. Dyn. Syst. 37 (2017), no. 10, 5355–5365.

9. A new class of traveling solitons for cubic fractional nonlinear Schrödinger equations (with Yannick Sire), Nonlinearity 30 (2017) 1262–1286.

8. Global well-posedness of the NLS system for infinitely many fermions (with Thomas Chen and Nataša Pavlović), Arch. Ration. Mech. Anal. 224 (2017), no. 1, 91–123.

7. Dispersive and Strichartz estimates for the three-dimensional wave equation with a scaling-critical class of potential (with The Anh Bui and Xuan Thinh Duong), J. Funct. Anal. 271 (2016), no. 8, 2215-2246.

6. Scattering for a nonlinear Schrödinger equation with a potential, Commun. Pure Appl. Anal. 15 (2016), no. 5, 1571-1601.

5. On dispersive blow-ups for the nonlinear Schrödinger equation (with Maja Taskovic), Differential Integral Equations 29 (2016), no. 9-10, 875-888.

4. A spectral multiplier theorem associated with a Schrödinger operator, J. Fourier Anal. Appl. 22 (2016), no. 3, 591-622.

3. Uniqueness of solutions to the 3D quintic Gross-Pitaevskii hierarchy (with Kenneth Taliaferro and Zhihui Xie), J. Funct. Anal. 270 (2016), no. 1, 34-67.

2. On fractional Schrödinger equations in Sobolev spaces (with Yannick Sire), Commun. Pure Appl. Anal. 14 (2015), no. 6, 2265-2282

1. Unconditional uniqueness of the cubic Gross-Pitaevskii hierarchy with low regularity (with Kenneth Taliaferro and Zhihui Xie), SIAM J. Math. Anal. 47 (2015), no. 5, 3314-3341.