27. Large N limit and 1/N expansion of invariant observables in O(N) linear σ-model via SPDE
(wih Hao Shen, Xiangchan Zhu)
To appear in Probability Theory and Related Fields
26. Surface quasi-geostrophic equation perturbed by derivatives of space-time white noise
（with Martina Hofmanová, Xiaoyutao Luo, Xiangchan Zhu）
Mathematische Annalen 390:5111-5152, 2024.
25. Singular kinetic equations and applications
(with Zimo Hao, Xicheng Zhang, Xiangchan Zhu)
The Annals of Probability Vol. 52, No. 2, 576–657, 2024.
24. A new derivation of the finite N master loop equation for lattice Yang-Mills
(with Hao Shen, Scott Smith)
Electron. J. Probab. 29 no. 29, 1–18, 2024.
(with Zhenfu Wang, Xianliang Zhao)
Archive for Rational Mechanics and Analysis, (2023) 247:101
22. A class of supercritical/critical singular stochastic PDEs: Existence, non-uniqueness, non-Gaussianity, non-unique ergodicity.
(With Martina Hofmanova, Xiangchan Zhu)
J. Funct. Anal. 285(2023), no. 5, Paper No. 110011. 60 (35)
(With Martina Hofmanova, Xiangchan Zhu)
J. Eur. Math. Soc. 26, 163–260 (2024)
(With Martina Hofmanova, Xiangchan Zhu)
Archive for Rational Mechanics and Analysis, 247 (2023),no. 3, Paper No. 46.
19. A Stochastic Analysis Approach to Lattice Yang–Mills at Strong Coupling
(With Hao Shen, Xiangchan Zhu)
Communications in Mathematical Physics, 400 (2023), no. 2, 805–851
18. Global-in-time probabilistically strong and Markov solutions to stochastic 3D Navier-Stokes equations: existence and non-uniqueness
(With Martina Hofmanova, Xiangchan Zhu)
The Annals of Probability, 2023, Vol. 51, No. 2, 524-579
17. An SPDE approach to perturbation theory of Φ42: asymptoticity and short distance behavior
(With Hao Shen, Xiangchan Zhu)
The Annals of Applied Probability, 33(4): 2600-2642, 2023
16. Large N Limit of the O(N) Linear Sigma Model in 3D,
(With Hao Shen, Xiangchan Zhu),
Communications in Mathematical Physics . 394 no.3, 953–1009. 2022
15. Singular HJB equations with applications to KPZ on the real line,
(With Xicheng Zhang, Xiangchan Zhu),
Probability Theory and Related Fields. 183 no. 3-4, 789–869,2022
14. Large N Limit of the O(N) Linear Sigma Model via Stochastic Quantization,
(With Hao Shen, Scott Smith, Xiangchan Zhu)
The Annals of Probability, 50(1), 131-202, 2022.
13. On ill- and well-posedness of dissipative martingale solutions to stochastic 3D Euler equations
(With Martina Hofmanova, Xiangchan Zhu)
Commun. Pure Appl. Math. Vol. LXXV, 2446–2510 (2022)
12. Conservative stochastic 2-dimensional Cahn-Hilliard equation,
(With Michael Rockner, Huanyu Yang)
The Annals of Applied Probability, Vol. 31, No. 3, 1336-1375, 2021.
11. Stochastic heat equation for infinite string with values in manifold,
(With Xin Chen, Bo Wu, Xiangchan Zhu),
Transactions of the American Mathematical Society, 374(1):407-452, 2021.
10. Stochastic Heat Equations with Values in a Manifold via Dirichlet Forms,
(With Michael Rockner, Bo Wu, Xiangchan Zhu),
SIAM J. Math. Anal., 52(3):2237-2274, 2020.
9. Dirichlet form associated with the Φ43 model,
(With Xiangchan Zhu)
Electron. J. Probab. 23, no. 78, 1-31, 2018.
8. Lattice approximation to the dynamical Φ43 model,
(With Xiangchan Zhu)
Ann. Probab. 46 no. 1, 397-455, 2018.
7. Ergodicity for the Stochastic Quantization Problems on the 2D-Torus. (With Michael Röckner, Xiangchan Zhu)
Comm. Math. Phys. 352 no. 3, 1061–1090, 2017
6. Restricted Markov uniqueness for the stochastic quantization of P(Φ)2 and its applications.
(With Michael Röckner, Xiangchan Zhu)
J. Funct. Anal. 272 no. 10, 4263-4303, 2017.
5. Random attractor associated with the quasi-geostrophic equation.
(With Xiangchan Zhu)
J. Dynam. Differential Equations 29, no. 1, 289–322, 2017.
4. Three dimensional Navier-Stockes equation driven by space-time white noise.
(With Xiangchan Zhu)
Journal of Differential Equations, 259, 4443–4508, 2015.
3. Sub- and supercritical stochastic quasi-geostrophic equation,
(With Michael Röckner, Xiangchan Zhu)
The Annals of Probability, 43, No. 3, 1202–1273, 2015.
2. Local existence and non-explosion of solutions for stochastic fractional partial differential equations driven by multiplicative noise,
(With Michael Röckner, Xiangchan Zhu)
Stochastic Processes and their Applications, 124 1974–2002, 2014.
1. The stochastic reflection problem on a convex set of a Hilbert space and BV functions in a Gelfand triple,
(With Michael Röckner, Xiangchan Zhu)
The Annals of Probability, 40, 1759-1794, 2012.
