个人简介

教育经历


2010.10–2012.3, 比勒菲尔德大学, 数学, 博士, 导师: Michael Rockner

2007.9–2012.7, 北京大学, 概率论和数理统计, 博士, 导师: 马志明

2003.9–2007.7, 四川大学, 数学与应用数学（基础）, 学士


科研与学术工作经历


2021.01-今     中国科学院数学与系统科学研究院, 应用数学所,研究员

2019.10-2020.12  中国科学院数学与系统科学研究院, 应用数学所,副研究员

2016.03-2020.04  德国Bielefeld大学 W1教授,

2016.01-2019.09  北京交通大学, 理学院, 副教授

2014.05-2015.12  北京交通大学, 理学院, 讲师

2012.06-2014.05  北京交通大学, 博士后


研究方向

随机偏微分方程
奇异随机偏微分方程，随机量子化方程，KPZ方程，随机Navier-Stokes方程，随机欧拉方程, 随机反射问题
随机分析
狄氏型

学术论文

  1. Surface quasi-geostrophic equation perturbed by derivatives of space-time white noise

    Martina Hofmanová, Xiaoyutao Luo, Rongchan Zhu, Xiangchan Zhu, To appear in Mathematische Annalen

  2. Singular kinetic equations and applications

    Zimo Hao, Xicheng Zhang, Rongchan Zhu, Xiangchan Zhu, The Annals of probability, 52 (2024) 2 576-657

  3. Sharp non-uniqueness of solutions to stochastic Navier-Stokes equations

    Weiquan Chen, Zhao Dong, Xiangchan Zhu, SIAM J. Math. Anal.,56 (2024) 2 2248-2285

  4. Non-uniqueness in law of stochastic 3D Navier--Stokes equations

    Martina Hofmanov′a, Rongchan Zhu, and Xiangchan Zhu. J. Eur. Math. Soc. 26, 163–260 (2024)

  5. Global-in-time probabilistically strong solutions to stochastic power-law equations: existence and non-uniqueness

    Huaxiang Lü, Xiangchan Zhu, Stochastic Processes and their Applications 164 (2023) 62-98

  6. A class of supercritical/critical singular stochastic PDEs: existence, non-uniqueness, non-Gaussianity, non-unique ergodicity

    M. Hofmanova, R. Zhu, X. Zhu, J. Funct. Anal. 285(2023), no.5, Paper No. 110011.60(35)

  7. Global existence and non-uniqueness for 3D Navier-Stokes equations with space-time white noise.

    Martina Hofmanov′a, Rongchan Zhu, and Xiangchan Zhu. Archive for Rational Mechanics and Analysis, 247 (2023), no.3, paper No. 46.

  8. Global-in-time probabilistically strong and Markov solutions to stochastic 3D Navier--Stokes equations: existence and non-uniqueness

    M. Hofmanova, R. Zhu, X. Zhu, The Annals of probability, 2023, Vol. 51, No. 2, 524-579

  9. A Stochastic Analysis Approach to Lattice Yang–Mills at Strong Coupling

    Hao Shen, Rongchan Zhu, Xiangchan Zhu, Communications in Mathematical Physics, 400 (2023), no. 2, 805-851

  10. An SPDE approach to perturbation theory of Φ42: asymptoticity and short distance behavior

    Hao Shen, Rongchan Zhu, Xiangchan Zhu, The Annals of applied probability, 33(4):2600-2642, 2023

  11. Large deviation principle for the two-dimensional stochastic Navier-Stokes equations with anisotropic viscosity

    B. Chen, X. Zhu, Acta Mathematicae Applicatae Sinica (English Series) Vol 39, No. 3 (2023) 511-549

学术论文

  1. On ill- and well-posedness of dissipative martingale solutions to stochastic 3D Euler equations

    M. Hofmanova, R. Zhu, X. Zhu, Commun. Pure Appl. Math Vol. LXXV, 2446–2510 (2022)

  2. Large N limit of the O(N) linear sigma model in 3D

    Hao Shen, Rongchan Zhu, Xiangchan Zhu, Communications in Mathematical Physics 394 no.3, 953–1009.2022

  3. Singular HJB equations with applications to KPZ on the real line

    Xicheng Zhang, Rongchan Zhu, Xiangchan Zhu, Probability Theory and Related Fields 183 (2022), no. 3-4, 789–869

  4. Large N limit of the O(N) linear sigma model via stochastic quantization

    H. Shen, S. Smith, R. Zhu, X. Zhu, The Annals of Probability 2022, Vol. 50, No. 1, 131–202

  5. Stochastic heat equation for infinite string with values in manifold

    X. Chen, B. Wu, R. Zhu, X. Zhu, Transactions of the American Mathematical Society 374 (1) 407-452, 2021

  6. Weak universality of the dynamical Φ43 moedl on the whole space

    Rongchan Zhu, Xiangchan Zhu Potential Anal (2021). https://doi.org/10.1007/s11118-021-09941-0

  7. Stochastic Heat Equations with Values in a Manifold via Dirichlet Forms

    M. Rockner, B. Wu, R. Zhu, X. Zhu, SIAM J. Math. Anal., 52(3):2237-2274, 2020.

  8. Piecewise linear approximation for the dynamical Φ43 model

    R. Zhu, X. Zhu, Sci China Math, 2020, 63: 381-410.

  9. On the small time asymptotics of the dynamical Φ41 model

    B. Chen, X. Zhu, Acta Math Sinica 2020

  10. A remark on global solutions to random 3D vorticity equations for small initial data

    M. Rockner, R. Zhu, X. Zhu, DCDS-B 2019, 24(8): 4021-4030.

  11. Lattice approximation to the dynamical Φ43 model

    R. Zhu, X. Zhu, Ann. Probab. 46 (2018), no. 1, 397-455.

  12. Stochastic Heat Equations with Values in a Riemannian Manifold

    M. Rockner, B. Wu, R. Zhu, X. Zhu, Rendiconti Lincei Matematicae Applicazioni, 29 (2018), no. 1, 205-213.

  13. Dirichlet form associated with the Φ43 model

    R. Zhu, X. Zhu, Electron. J. Probab. 23 (2018), no. 78, 1-31.

  14. Restricted Markov uniqueness for the stochastic quantization of P(Φ)2 and its applications

    M. Rockner, R. Zhu, X. Zhu, J. Funct. Anal. (2017), 272 (10), 4263-4303.

  15. Ergodicity for the stochastic quantization problems on the 2D-torus

    M. Rockner, R. Zhu, X. Zhu, Comm. Math. Phys., 352 (3) 1061–1090, 2017.

  16. Random attractor associated with the quasi-geostrophic equation

    R. Zhu, X. Zhu, Journal of Dynamical and Differential Equations, 29,1, 289–322, (2017)

  17. Approximating three-dimensional Navier-Stokes equations driven by space-time white noise

    R. Zhu, X. Zhu, IDAQP, 20 (2017), no. 4, 1750020, 77 pp.

  18. Three-dimensional Navier-Stokes equations driven by space-time white noise

    R. Zhu, X. Zhu, Journal of Differential Equations , 259, 9, 5, 2015, 4443–4508.

  19. Recent Progress on the Dirichlet Forms Associated with Stochastic Quantization Problems

    R. Zhu, X. Zhu, Springer Proceedings in Mathematics and Statistics, v229, 561-571 Stochastic Partial Differential Equations and Related Fields-In Honor of Michael Rockner.

  20. Sub and supercritical stochastic quasi-geostrophic equation

    M. Rockner, R. Zhu, X. Zhu, The Annals of Probability, (2015), 43 (3), 1202–1273.

  21. Existence and uniqueness of solutions to stochastic functional differential equations in infinite dimensions

    M. Rockner, R. Zhu, X. Zhu, Nonlinear Analysis: Theory, Methods Applications 125, (2015), 358–397.

  22. BV functions in a Gelfand triple for differentiable measure and its applications

    M. Rockner, R. Zhu, X. Zhu, Forum Mathematicum. 27, 3,(2015) 1657–1687

  23. Martingale solutions for stochastic active scalar equations perturbed by non-trace class noise

    R. Zhu, X. Zhu, IDAQP, 17, 2 (2014) (32 pages)

  24. Local existence and non-explosion of solutions for stochastic fractional partial differential equations driven by multiplicative noise

    M. Rockner, R. Zhu, X. Zhu, Stochastic Processes and their Applications 124(5) (2014), 1974–2002

  25. A note on stochastic semilinear equations and their associated Fokker-Planck equations

    M. Rockner, R. Zhu, X. Zhu, J. Math. Anal. Appl. 415(1) (2014), 83–109.

  26. Large deviation principles for the stochastic quasi-geostrophic equation

    W. Liu, M. Rockner, X. Zhu, Stoch. Proc. Appl. 123(8) (2013), 3299–3327.

  27. The stochastic reflection problem on a convex set of a Hilbert space and BV functions in a Gelfand triple

    M. Rockner, R. Zhu, X. Zhu, The Annals of Probability 40(4) (2012), 1759–1794

  28. Stochastic Quasi-Geostrophic Equation (Announcement)

    M. Rockner, R. Zhu, X. Zhu, IDAQP 15(1) (2012), 6 pages.

  29. BV functions in a Gelfand triple and the stochastic reflection problem on a convex set of a Hilbert space

    M. Rockner, R. Zhu, X. Zhu, Comptes Rendus Mathematique 348(21–22) (2010), 1175–1178.

  30. On notions of harmonicity for non-symmetric Dirichlet form

    Z. Ma, R. Zhu, X. Zhu, Science China Mathematics 53(6) (2010), 1407–1420

学术链接

  1. stochastic webinar

联系方式

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