**Yuzhao Wang**

· *Associate** Professor
in Mathematics*

**Mailing
Address**:

School of Mathematics

Watson Building

University of Birmingham

Edgbaston,

Birmingham,

B15 2TT,

United Kingdom

**e-mail**: y dot wang dot 14 [at] bham.ac.uk

**Brief
CV | Publications
| Teaching
| Links **

I am an Associate 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

**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 \(\ell^2\) decoupling theory.

**Seminars:** Analysis
Seminar at UoB, Analysis Seminar at UoE, UoE seminars, ICMS events,
London Analysis and
Probability Seminar, One-day workshop 2022, Workshop: random dispersive PDEs 2023

**Summer Research Projects (for students):** Summer Research Projects 2023

·
(with I. Chevyrev, T. Oh) Norm inflation for the cubic nonlinear
heat equation above the scaling critical regularity, arXiv:2205.14488.

· (with R. Liang) Gibbs measure for the focusing
fractional NLS on the torus.. arXiv:2109.05626, 19 pages

· (with T. Oh, Y. Zine) Three-dimensional
stochastic cubic nonlinear wave equation with almost space-time white noise
(arXiv link),
**Stoch. Partial Differ. Equ. Anal. Comput.** (2022) Special issue dedicated to Professor
Istvan Gyongy on the occasion of
his seventieth birthday. doi: 10.1007/s40072-022-00237-x

· (with T. Oh, T. Robert, N. Tzvetkov) Stochastic
quantization of Liouville conformal field theory, arXiv:2004.04194, 77
pages.

· (with T. Oh, T. Robert, P. Sosoe) Invariant
Gibbs dynamics for the dynamical sine-Gordon model, **Proc. Roy. Soc.
Edinburgh Sect. A** 151 (2021), no. 5, 1450--1466.

· (with T. Oh, T. Robert) On the parabolic and hyperbolic
Liouville equations, **Comm. Math. Phys.** 387 (2021), no. 3,
1281--1351.

· (with T. Oh, T. Robert, and P. Sosoe) On the
two-dimensional hyperbolic stochastic sine-Gordon equation, **Stoch.
Partial Differ. Equ. Anal. Comput.**
9 (2021), no. 1, 1--32.

· (with T. Oh) On global well-posedness
of the modified KdV equation in modulation spaces,
**Discrete Contin. Dyn. Syst. A** 41 (2021), no.
6, 2971--2992.

· (with W. Wang) Liouville-type theorems for the
stationary MHD equations in 2D, **Nonlinearity** 32 (2019), no. 11,
4483--4505.

· (with T. Oh, O. Pocovnicu)
On the stochastic nonlinear
Schrödinger equations with non-smooth additive noise, **Kyoto J.
Math.** 60 (2020), no. 4, 1227--1243.

· (with T. Oh) Global well-posedness
of the one-dimensional cubic nonlinear Schrödinger equation in almost
critical spaces, **J. Differential Equations** 269 (2020), no. 1,
612--640.

· (with T. Oh) Normal form approach to the
one-dimensional periodic cubic nonlinear Schrödinger equation in almost
critical Fourier-Lebesgue spaces, **J. Anal. Math.** 143 (2021), no. 2,
723--762.

· (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, **J. Aust.
Math. Soc.** 109 (2020), no. 1, 44--67.

· (with R. Mosincat,
O. Pocovnicu, L. Tolomeo)
Global well-posedness of three-dimensional periodic
stochastic nonlinear beam equations.

· (with T. Oh, N. Tzvetkov)
Solving the 4NLS with white noise
initial data, **Forum Math. Sigma** 8 (2020), Paper No. e48, 63 pp.

· (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.** 8 (2019), no. 1, 203--224.

· (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.

o Rui Liang (University of
Birmingham, since 2020).

o Guopeng
Li (Maxwell Institute and
University of Edinburgh, since 2019), joint with T. Oh (University of
Edinburgh).

o Rui Liang (University of Birmingham,
January to July 2019).

o Tomoyuki Tanaka (supported by JSPS and EPSRC,
since September 2021).

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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

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