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Mailing Address
The Watson Building
University of Birmingham
Edgbaston
Birmingham
B15 2TT
UK

Research Interest: Analysis Group at UoB   

Nonlinear Partial Differential Equations and Harmonic Analysis. In particular, the study of nonlinear dispersive PDEs such as nonlinear Schrödinger equations, nonlinear wave equations, and the KdV equation by using techniques from PDEs, Harmonic Analysis, and Probability theory. Mainly, well-posedness (existence, uniqueness, and stability of solutions) in both deterministic and probabilistic settings, existence of invariant measures, Strichartz estimates in different settings, etc. Also, interested in Fourier restriction theory and decoupling theory.


Seminars: Analysis seminar at UoB


Papers:

  1. (with R. Mosincat, O. Pocovnicu, L. Tolomeo) Global well-posedness of three-dimensional periodic stochastic nonlinear beam equations.
  2. (with T. Oh, N. Tzvetkov) Invariance of the white noise for the cubic fourth order nonlinear Schrödinger equation on the circle.
  3. (with T. Oh) Global well-posedness of the periodic cubic fourth order NLS in negative Sobolev spaces. arXiv:1707.02013.
  4. (with T. Oh) On the ill-posedness of the cubic nonlinear Schrödinger equation on the circle to appear in An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.)
  5. (with J. Xiao) A Liouville problem for the stationary fractional Navier-Stokes-Poisson system. J. J. Math. Fluid Mech. (2017). https://doi.org/10.1007/s00021-017-0330-9
  6. (with Z. Guo, Y. Sire, L. Zhao)  On the energy-critical fractional Schrödinger equation in the radial case. arXiv:1310.6816.
  7. (with J. Xiao) Well/ill-posedness for the dissipative Navier-Stokes system in generalized Carleson measure spaces, Adv. Nonlinear Anal. https://doi.org/10.1515/anona-2016-0042
  8. (with J. Xiao) A constructive approach to positive solutions of $\Delta_p f + f(u) \le 0$ on Riemannian manifolds, Ann. Inst. H. Poincaré Anal. Non Linéaire 33 (2016), no. 6, 1497--1507.
  9. (with J. Xiao) A uniqueness principle for $u^p \le (-\Delta)^{\alpha} u$ in the Euclidean space, Commun. Contemp. Math. 18 (2016), no. 6, 1650019, 17 pp.
  10. (with Y. Liu, J. Xiao) Nonnegative solutions of a fractional sub-Laplacian differential inequality on Heisenberg group, Dyn. Partial Differ. Equ. 12 (2015), no. 4, 379--403.
  11. (with J. Xiao) Homogeneous Campanato-Sobolev classes, Appl. Comput. Harmon. Anal. 39 (2015), no. 2, 214--247.
  12. (with Z. Guo, T. Oh) Strichartz estimates for Schrödinger equations on irrational tori, Proc. Lond. Math. Soc. 109 (2014), no. 4, 975--1013.
  13. (with Z. Guo) Improved Strichartz estimates for a class of dispersive equations in the radial case and their applications to nonlinear Schrödinger and wave equations. J. Anal. Math. 124 (2014), 1--38.
  14. (with L. Molinet) Dispersive limit from the Kawahara to the KdV equation, J. Differential Equations 255, (2013), 2196--2219.
  15. Periodic nonlinear Schrödinger equation in critical $H^s(\T^d)$ space, SIAM J. Math. Anal. 45, (2013), 1691--1703.
  16. Periodic Cubic Hyperbolic Schrödinger equation on $H^s(\T^2)$, J. Funct. Anal. 265 (2013), 424--434.
  17. Local well-posedness for hyperbolic-elliptic Ishimori equation, Nonlinear Anal. 75 (2012), 2534--2541.
  18. Quadratic dispersive generalized Benjamin-Ono equation, J. Math. Anal. Appl. 387 (2012), 844--856.
  19. Global well-posedness and scattering for derivative Schrödinger equation, Comm. Partial Differential Equations 36 (2011), 1694--1722.
  20. (with Z. Guo, L. Peng, B. Wang) Uniform well-posedness and inviscid limit for the Benjamin-Ono-Burgers equation, Adv. in Math. 228 (2011), 647--677.
  21. (with Z. Guo) On the well-posedness of the Schrödinger-KdV system, J. Differential Equations 249 (2010), 2500--2520.
  22. The Cauchy problem for the elliptic-hyperbolic Davey-Stewartson system in Sobolev space, J. Math. Anal. Appl. 367 (2010), 174--192.

Subpages (1): Brief CV
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