School of Mathematics

Watson Building

University of Birmingham

Edgbaston,

Birmingham,

B15 2TT,

United Kingdom

I am a Lecturer (tenured assistant professor) at the University of Birmingham, School of Mathematics. Previously, I held research positions at the University of Edinburgh (where I worked with Tadahiro Oh), and Memorial University (where I worked with Jie Xiao). I received my PhD from Peking University under the supervision of Carlos Kenig and Baoxiang Wang.

Curriculum Vitae: CV

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 \(\ell^2\) decoupling theory.

- (with T. Oh, T. Robert) On the parabolic and hyperbolic Liouville equations.
- (with T. Oh, T. Robert, and P. Sosoe) On the two-dimensional hyperbolic stochastic sine-Gordon equation.
- (with T. Oh) On global well-posedness of the modified KdV equation in modulation spaces.
- (with W. Wang)
Liouville-type theorems for the stationary MHD equations in 2D.
to appear in
**Nonlinearity** - (with T. Oh, O. Pocovnicu)
On the stochastic nonlinear Schrödinger equations
with non-smooth additive noise,
to appear in
**Kyoto J. Math.** - (with T. Oh) Global well-posedness of the one-dimensional cubic nonlinear Schrödinger equation in almost critical spaces.
- (with T. Oh)
Normal form approach to the one-dimensional periodic cubic nonlinear Schrödinger equation
in almost critical Fourier-Lebesgue spaces,
to appear in
**J. Anal. Math.** -
(with O. Pocovnicu)
An \(L^p\)-theory for almost sure local well-posedness of the nonlinear Schrödinger equations,
**C. R. Math. Acad. Sci. Paris**356 (2018), no. 6, 637--643. - (with J. Forlano, T. Oh)
Stochastic cubic nonlinear Schrödinger equation
with almost space-time white noise,
to appear in
**J. Aust. Math. Soc.** - (with R. Mosincat, O. Pocovnicu, L. Tolomeo) Global well-posedness of three-dimensional periodic stochastic nonlinear beam equations.
- (with T. Oh, N. Tzvetkov) Invariance of the white noise for the cubic fourth order nonlinear Schrödinger equation on the circle.
- (with T. Oh)
Global well-posedness of the periodic cubic fourth order NLS
in negative Sobolev spaces
(arXiv link),
**Forum Math. Sigma**6 (2018), e5, 80 pp. - (with T. Oh)
On the ill-posedness of the cubic nonlinear
Schrödinger equation on the circle
**An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.)**64 (2018), no. 1, 53--84. -
(with J. Xiao)
A Liouville problem for the stationary fractional Navier-Stokes-Poisson system,
**J. Math. Fluid Mech.**20 (2018), no. 2, 485--498. -
(with Z. Guo, Y. Sire, L. Zhao)
On the energy-critical fractional Schrödinger equation in the radial case,
(arXiv link)
**Dyn. Partial Differ. Equ.**15 (2018), no. 4, 265--282. -
(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 -
(with J. Xiao)
A constructive approach to positive solutions of \(\Delta_p u + f(u,\nabla u) \le 0\)
on Riemannian manifolds,
**Ann. Inst. H. Poincaré Anal. Non Linéaire**33 (2016), no. 6, 1497--1507. -
(with J. Xiao)
A uniqueness principle for \(u^p\leq(-\Delta)^{\frac\alpha 2}u\) in the Euclidean space,
**Commun. Contemp. Math.**18 (2016), no. 6, 1650019, 17 pp. -
(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. -
(with J. Xiao)
Homogeneous Campanato-Sobolev classes,
**Appl. Comput. Harmon. Anal.**39 (2015), no. 2, 214--247. -
(with Z. Guo, T. Oh)
Strichartz estimates for Schrödinger equations on irrational tori,
**Proc. Lond. Math. Soc.**109 (2014), no. 4, 975--1013. -
(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. -
(with L. Molinet)
Dispersive limit from the Kawahara to the KdV equation,
**J. Differential Equations**255, (2013), 2196--2219. -
Periodic nonlinear Schrödinger equation in critical \(H^s(\mathbb{T}^n)\) spaces,
**SIAM J. Math. Anal.**45, (2013), 1691--1703. -
Periodic Cubic Hyperbolic Schrödinger equation on \(\mathbb{T}^2\),
**J. Funct. Anal.**265 (2013), 424--434. -
Local well-posedness for hyperbolic-elliptic Ishimori equation,
**J. Differential Equations**252 (2012), 4625--4655. -
Quadratic dispersive generalized Benjamin-Ono equation,
**J. Math. Anal. Appl.**387 (2012), 844--856. -
Global well-posedness and scattering for derivative Schrödinger equation,
**Comm. Partial Differential Equations**36 (2011), 1694--1722. -
(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. -
(with Z. Guo)
On the well-posedness of the Schrödinger-KdV system,
**J. Differential Equations**249 (2010), 2500--2520. -
The Cauchy problem for the elliptic-hyperbolic Davey-Stewartson system in Sobolev space,
**J. Math. Anal. Appl.**367 (2010), 174--192.

- Terence Tao, What's new,
- arXiv
- MathSciNet
- Sherpa/Romeo

Seminars at: - Peking University, BICMR,
- School of Mathematics, Peking University

- Fields Institute

- Heriot Watt University,
Maxwell Institute,
ICMS,
Royal Society of Edinburgh

Societies: - London Mathematical Society
- Edinburgh Mathematical Society
- Institute of Mathematics and its Applications (UK)
- American Mathematical Society
- Society for Industrial and Applied Mathematics
- European Mathematical Society
- International Mathematical Union
- Einstein Field Equations - for beginners
- International Winter School on Gravity and Light 2015

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