Research
Publications / Preprints
Most preprints are available at arXiv
22. (with Kiyeon Lee) Energy solutions for the fifth-order modified Korteweg de-Vries equations, accepted for publication in DCDS
21. (with Capistrano-Filho and Vielma Leal) On the control issues for higher-order nonlinear dispersive equations on the circle, On the control issues for higher-order nonlinear dispersive equations on the circle, Nonlinear Analysis : Real World Applications Volume 68, December 2022, 103695 , https://doi.org/10.1016/j.nonrwa.2022.103695
20. (with Hong and Yang) Strichartz estimates for higher-order Schr\"odinger equations and their applications , Journal of Differential Equations 324 (2022) 41--75. https://doi.org/10.1016/j.jde.2022.03.040
19. (with Hong and Yang) On the continuum limit for the discrete Nonlinear Schr\"odinger equation on a large finite cubic lattice, Nonlinear Analysis Volume 227, February 2023, 113171 https://doi.org/10.1016/j.na.2022.113171
18. (with Christopher Maulén) Ill-posedness issues on $(abcd)$-Boussinesq system, online available in Journal of Dynamics and Differential Equations https://doi.org/10.1007/s10884-022-10189-4 pdf
17. (with Hong and Yang) Korteweg-de Vries limit for the Fermi-Pasta-Ulam system, Arch. Ration. Mech. Anal. 240 (2021), no. 2, 1091--1145 pdf
16. (with Hong, Nakamura and Yang) Finite difference scheme for two-dimensional periodic nonlinear Schrödinger equations, Journal of Evolution Equations, 21 (2021) no. 1, 391--418. https://doi.org/10.1007/s00028-020-00585-y pdf
15. Well-posedness issues on the periodic modified Kawahara equation, Annales de l'Institut Henri Poincar\'e C, Analyse Non Lin\'eaire 37(2020) 373--416 https://doi.org/10.1016/j.anihpc.2019.09.002 pdf
14. (with Claudio Muñoz) Asymptotic dynamics for the small data weakly dispersive one-dimensional Hamiltonian ABCD system, Transactions of the American Mathematical Society Vol. 373, No. 2, (2020), Pages 1043--1107 https://doi.org/10.1090/tran/7944 pdf
13. (With Miguel A. Alejo) Global solutions and stability properties of the 5th order Gardner equation, Journal of Dynamics and Differential Equations 35, pages575--621 (2023) https://doi.org/10.1007/s10884-021-10022-4
12. (with Miguel A. Alejo, Manuel Fernando Cortez and Claudio Muñoz) On the dynamics of zero-speed solutions for Camassa-Holm type equations, International Mathematics Research Notices (2021) no. 9, 6543--6585. doi:10.1093/imrn/rnz038. pdf
11. (with Márcio Cavalcante) Local well-posedness of the fifth-order KdV-type equations on the half-line, Communications on Pure and Applied Analysis 2019, 18(5): 2607--2661 doi: 10.3934/cpaa.2019117 pdf
10. (with Márcio Cavalcante) The initial-boundary value problem for the Kawahara equation on the half-line, Nonlinear Differential Equations and Applications (NoDEA), 27 (2020), no. 5, Paper No. 45, 50 pp. DOI: 10.1007/s00030-020-00648-6. pdf
9. (with Gyeongha Hwang) Probabilistic global well-posedness of generalized KdV, submitted. pdf
8. (with Claudio Muñoz) Extended decay properties for generalized BBM equations, "Nonlinear Dispersive Partial Equations and Inverse Scattering", Peter D. Miller, Peter Perry, Jean-Claude Saut, Catherine Sulem Eds, Fields Institute Communications 83, Springer (2019). pdf
7. (with Claudio Muñoz, Felipe Poblete and Juan C. Pozo) The scattering problem for Hamiltonian ABCD Boussinesq systems in the energy space, Journal de Mathématiques Pures et Appliquées, 127 (2019) 121-159, https://doi.org/10.1016/j.matpur.2018.08.005. pdf
6. Low regularity Cauchy problem for the fifth-order modified KdV equations on $\mathbb{T}$, Journal of Hyperbolic Differential Equations Vol. 15, No. 3 (2018) 463--557. http://dx.doi.org/10.1142/S0219891618500170. pdf
5. Periodic fourth-order cubic NLS : Local well-posedness and Non-squeezing property, Journal of Mathematical Analysis and Applications 461 2 (2018) 1327-1364. pdf
4. (with Gyeongha Hwang) Probabilistic well-posedness of generalized KdV, Proc. Amer. Math. Soc. 146 (1) (2018) 267-280. pdf
3. (with Sunghyun Hong) Global well-posedness and Nonsqueezing property for the higher-order KdV-type flow, Journal of Mathematical Analysis and Applications 441, 1, (2016), 140-166. pdf
2. Local well-posedness for the fifth-order KdV equations on $\mathbb{T}$, Journal of Differential Equations 260, 10, (2016), 7683-7737. pdf
1. (with Zihua Guo, Soonsik Kwon) Rough solutions of the fifth-order KdV equations, Journal of Functional Analysis 265, 11, (2013), 2585-2990. pdf