Research

Most preprints are available at arXiv.org.

  • On the fifth order KdV equation: Local well-posedness and lack of uniform continuity of the solution map, Journal of Differential Equations, (2008) 245(9) pp. 2627-2659.
  • Well-posedness and ill-posedness of the fifth order modified KdV equation, Electronic Journal of Differential Equations, Vol. 2008(2008), No. 01, pp. 1-15.
  • with Myeongju Chae, Global well-posedness for the L2 critical Hartree equation on Rn, n ≥ 3, Communications on Pure and Applied Analysis, 8(2009), no.6, 1725–1743.
  • with Rowan Killip, Shuanglin Shao, and Monica Visan, On the mass-critical generalized KdV equation, Discrete and Continuous Dynamical Systems, Series A, 32(2012), no. 1, 191–221.
  • with Tristan Roy, Bilinear local smoothing estimate for Airy equation, Differential and Integral Equations, 25(2012), No.1-2, 75–83.
  • with James Colliander and Tadahiro Oh, A remark on normal forms and the upside-down I-method for periodic NLS: Growth of higher Sobolev norms, Journal d’Analyse Math ́ematique, 118(2012), 55-82.
  • with Tadahiro Oh, On unconditional well-posedness of modified KdV equation, International Mathematical Research Notice, 2012(2012), 26 pages, doi:10.1093/imrn/rnr156.
  • with Zihua Guo and Tadahiro Oh, Poincaré-Dulac normal form reduction for unconditional well-posedness of the periodic cubic NLS, Communications on Mathematical Physics, 322(2013), 19–48.
  • with Yonggeun Cho, Gyeongha Hwang, and Sanghyuk Lee, Profile decompositions and blowup phenomena of mass critical fractional Schrödinger equations, Nonlinear Analysis, TMA, 86(2013) 12–29.
  • with Zihua Guo and Chulkwang Kwak,  Rough solutions of the fifth-order KdV equations,  Journal of Functional Analysis 265 (2013) no.11 2791–2829
  • with Yonggeun Cho, Gyeongha Hwang, and Sanghyuk Lee, Profile decompositions of fractional Schr\”odinger equations with angularly regular data, Journal of Differential Equations 256 (2014), no. 8, 3011–-3037.
  • with Tristan Roy, Scattering of rough solutions of the nonlinear Klein-Gordon equations in 3D, Advances in differential equations 21(2016), no. 3, 333–372.
  • with Shuanglin Shao, Nonexistence of soliton-like solutions for defocusing generalized KdV equations, Electronic Journal of Differential Equations, Vol. 2015(2015) no. 51, 1–5.
  • with Yonggeun Cho, Gyeongha Hwang, and Sanghyuk Lee, On the finite time blowup for mass-critical Hartree equations, Royal Society of Edinburgh, Proceeding A. 145(2015) no.03, 467–479.
  • with Yonggeun Cho, Gyeongha Hwang, and Sanghyuk Lee, Well-posedness and ill-posedness for the cubic fractional Schrödinger equations, Discrete and Continuous Dynamical Systems, Series A. 35(2015) no.7, 2863–2880.
  •  with Myeongju Chae, The Stability of nonlinear Schrödinger equations with a potential in high Sobolev norms revisited, Communications in Pure and Applied Analysis, 15(2016), no. 2, 341–365.
  • with Sunho Choi, Modified scattering for the Vlasov-Poisson system, Nonlinearity 29(2016) no. 9 2755–2774.
  • with Yifei Wu, Orbital stability of solitary waves for derivative nonlinear Schrödinger equation, to appear in Journal d’Analyse Mathematique 135(2018) no.2, 473–486.
  • with Sung-hyun Hong, Nonsqeezing property of the coupled KdV type system without Miura transform, preprint.
  • with Jaywan Chung, Zihua Guo, Tadahiro Oh, Normal form approach to global well-posedness of the quadratic derivative Schrödinger equations on the circle, to appear in Annales de l’Institut Henri Poincaré (C) Analyse Non Linéaire 34(2017), no.5, 1273–1297.
  • with  Younghun Hong, and Haewon Yoon, Global existence versus finite time blowup dichotomy for the system of nonlinear Schrödinger equations, Journal de Mathématiques Pures et Appliquées 125(2019), 283–320.
  • with Kihyun Kim, Scattering of defocusing generalized Benjamin-Ono equations, Transactions of AMS 372(2019) no.7, 5011–5067.
  • with Tadahiro Oh and Haewon Yoon, Normal form approach to unconditional well-posedness of nonlinear dispersive PDEs on the real line, Annales de la Facult’e des Sciences de Toulouse: Mathématique, Série 6, 29(2020) no.3, 649–720.
  • with Kihyun Kim, On pseudoconformal blow-up solutions to the self-dual Chern-Simons-Schrödinger equation: existence, uniqueness, and instability, Memoirs of American Mathematical Society 284(2023), no.1409, v+128 pp.
  • with Kihyun Kim, Construction of blow-up manifolds to the equivariant self-dual Chern-Simons-Schrödinger equation, Annals of PDE 9 (2023) no.1, Paper No. 6, 129 pp.
  • with Kihyun Kim and Sung-Jin Oh, Blow-up dynamics for smooth finite energy radial data solutions to the self-dual Chern-Simons-Schrödinger equation,  to appear in Annales scientifiques de l’École normale supérieure, arXiv:2010.03252.
  • with Kihyun Kim and Sung-Jin Oh, Soliton resolution for equivariant self-dual Chern-Simons-Schrödinger equation in weighted Sobolev class, to appear in American Journal of Mathematics, arXiv:2202.07314.
  • with Yonggeun Cho, Kiyeon Lee, and Changhun Yang, Modified scattering of Dirac equations of scattering-critical nonlinearity, arXiv:2208.12040.

  • with Kiyeon Lee, and Changhun Yang, The modified scattering of 2 dimensional semi-relativistic Hartree equations, arXiv:2307.15886.