Research

Research Interests

Harmonic Analysis, Partial Differential Equations.

Papers and Preprints

  • Conditional existence of maximizers for the Tomas-Stein inequality for the sphere, arXiv: 2509:10754. With Ming Wang, Submitted in Oct. 2025.
  • A remark on the Strichartz inequality in one dimension, With R. Frier, arXiv: 2101:01148. Dynamics of Partial Differential Equations, 2022, Volume 19, No. 2, pages: 163--175.  
  • A remark on the two dimensional water wave problem with surface tension, with H.Shih. arXiv:1712.00090  Journal of Differential Equations, 2018.Oct.
  • On smoothness of extremizers of the Tomas-Stein inequality for S^1 arXiv:1601.07119, Preprint.
  • Linear profile decomposition for a family of fourth order Schrödinger equations arXiv:1410.7520, with J. Jiang, B.Stovall. arXiv: 1410:7520. Submitted in Oct. 2025.
  • On existence of extremizers for the Tomas-Stein inequality for S^1 arXiv:1507.04302, Journal of Functional Analysis 270 (2016), 3996-4038.
  • On one dimensional Quantum Zakharov system arXiv:1412.2882, with J. Jiang, C. Lin. Discrete and Continuous Dynamical Systems - A, 36 (10), 5445 --5475.
  • On Characterization of the sharp Strichartz inequality for the Schrödinger equation. arXiv:1404.0985 , with J. Jiang. Analysis & PDE 9-2 (2016), 353--361.
  • Nonexistence of soliton-like solutions for defocusing generalized KdV equations, arXiv:1205.0849, with S. Kwon. Electronic JDE, 2015(51), 1-5.
  • Analyticity of extremisers to the Airy Strichartz inequality, arXiv:1101.0012, with D. Hundertmark. Bulletin of the London Mathematical Society, (2012) 44(2): 336-352.
  • On the extremisers of an adjoint Fourier restriction inequality, arXiv:1006:4318 , with M. Christ. Advances in Mathematics, Volume 230, Issue 3, 20 June 2012, 957-977.
  • Existence of extremals for a Fourier restriction inequality, arXiv:1006:4319 , with M. Christ. Analysis & PDE, 5(2): 261-312,2012.
  • The linear profile decomposition for the fourth order Schrödinger equation, arXiv:0911:0719 , with J. Jiang and B. Pausader. J. Differential Equations 249 (2010) 2521--2547.
  • The low regularity global solutions for the critical generalized KdV equation, arXiv:0908:0782, with C. Miao, Y. Wu, and G. Xu. Dynamics of PDE, Vol.7, No.3, 265--288, 2010.
  • On the mass critical generalized KdV equation, arXiv:0907:5412 , with R. Killip, S. Kwon, and M. Visan. Discrete and Continuous Dynamical Systems - A, Vol.32 (2012), 1, 191-221.
  • The mass-critical fourth-order Schrödinger equation in high dimensions, arXiv:0906:1547, with B. Pausader. J. Hyperbolic DE, 7 (4), 651--705, 2010.
  • The linear profile decomposition for the Airy equation and the existence of maximizers for the Airy Strichartz inequality, arXiv:0809.0157. Analysis & PDE, Vol. 2 (2009), No. 1, 83--117.
  • Maximizers for the Strichartz inequalities and the Sobolev-Strichartz inequalities for the Schrödinger equation, arXiv:0809.0153. Electronic J. of Differential Equations, Vol. 2009 (2009), No. 03, 1--13.
  • A note on the restriction conjecture for the cone in the cylindrically symmetric case, arXiv:0710:1466. Proc. Amer. Math. Soc. 137 (2009), 135--143.
  • Sharp linear and bilinear restriction estimate for paraboloids in the cylindrically symmetric case, arXiv:0706:3759. Rev. Mat. Iberoamericana 25 (2009), no. 2, 1127--1168.
  • Integral operators with variable kernels on weak Hardy spaces, with Y. Ding and S.Lu. J. Math.Anal. Appl. 317 (2006), no. 1, 127--135.
  • On the Marcinkiewicz integral with variable kernels, with Y. Ding and C. Lin. Indiana Univ. Math.J. 53 (2004), no. 3, 805--821.