Yuzhao Wang

·  Associate Professor in Mathematics

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

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

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.

### Papers:

·

·       (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. &Scedil;tiin&tcedil;. Univ. Al. I. Cuza Ia&scedil;i. 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.

### Ph.D. Students:

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).

### Master Students:

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

### Postdoc:

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