个人简介


   罗德军,博士,中国科学院数学与系统科学研究院副研究员


教育背景
  2005.7--2008.9: 北京师范大学/Université de Bourgogne,联合培养博士
  2003.9--2005.7: 北京师范大学数学科学学院,理学硕士
  1999.9--2003.7: 北京师范大学数学科学学院,理学学士


工作经历
 
2018.12--2019.11: 意大利比萨高师,合作研究 
 
2017.5--2018.3: 意大利比萨大学数学系,合作研究 
 
2014.3--现在: 中国科学院数学与系统科学研究院 应用数学所 副研究员
 
2009.3--2011.2: University of Luxembourg   Mathematics Research Unit 博士后
 
2008.7--2014.2: 中国科学院数学与系统科学研究院  应用数学所 助理研究员


Preprints

  • Dejun Luo. Convergence of stochastic 2D inviscid Boussinesq equations with transport noise to a deterministic viscous system, arXiv:2008.01434.

  • Franco Flandoli, Dejun Luo. Cristiano Ricci. On the relation between the Girsanov transform and the Kolmogorov equations for SPDEs, arXiv:2006.06189.

  • Franco Flandoli, Martina Hofmanová, Dejun Luo, Torstein Nilssen. Global well-posedness of the 3D Navier--Stokes equations perturbed by a deterministic vector field, arXiv:2004.07528.

  • Dejun Luo, Rongchan Zhu. Stochastic mSQG equations with multiplicative transport noises: white noise solutions and scaling limit, arXiv:2004.06927.

  • Franco Flandoli, Dejun Luo. High mode transport noise improves vorticity blow-up control in 3D Navier-Stokes equations, arXiv:1910.05742.

  • Franco Flandoli, Dejun Luo. Point vortex approximation for 2D Navier--Stokes equations driven by space-time white noise, arXiv:1902.09338.


Recent Papers

  • Franco Flandoli, Dejun Luo, Cristiano Ricci. A numerical approach to Kolmogorov equation in high dimension based on Gaussian analysis. Journal of Mathematical Analysis and Applications (2020), accepted.

  • Franco Flandoli, Lucio Galeati, Dejun Luo. Scaling limit of stochastic 2D Euler equations with transport noises to the deterministic Navier-Stokes equations. Journal of Evolution Equations (2020), accepted.

  • Dejun Luo, Martin Saal. A scaling limit for the stochastic mSQG equations with multiplicative transport noises. Stochastics and Dynamics (2020), accepted.

  • Dejun Luo, Martin Saal. Regularization by noise for the point vortex model of mSQG equations. Acta Mathematica Sinica English Series (2020), accepted. 

  • Franco Flandoli, Francesco Grotto, Dejun Luo. Fokker-Planck equation for dissipative 2D Euler equations with cylindrical noise. Theory of Probability and Mathematical Statistics (2020), accepted.

  • Franco Flandoli, Dejun Luo. Convergence of transport noise to Ornstein-Uhlenbeck for 2D Euler equations under the enstrophy measure. Annals of Probability 48 (2020), no. 1, 264-295.

  • Franco Flandoli, Dejun Luo. Energy conditional measures and 2D turbulence. Journal of Mathematical Physics 61 (2020), no. 1, 013101, 22 pp.

  • Franco Flandoli, Dejun Luo. ρ-white noise solution to 2D stochastic Euler equations. Probability Theory and Related Fields 175 (2019), no. 3-4, 783-832.

  • Dejun Luo, Jian Wang. Refined basic couplings and Wasserstein-type distances for SDEs with Lévy noises. Stochastic Processes and their Applications 129 (2019), no. 9, 3129-3173.

  • Franco Flandoli, Dejun Luo. Euler-Lagrangian approach to 3D stochastic Euler equations. Journal of Geometric Mechanics 11 (2019), no. 2, 153-165.

  • Franco Flandoli, Dejun Luo. Kolmogorov equations associated to the stochastic two dimensional Euler equations. SIAM Journal on Mathematical Analysis 51 (2019), no. 3, 1761-1791.

  • Huaiqian Li, Dejun Luo. Quantitative stability estimates for Fokker-Planck equations. Journal de Mathématiques Pures et Appliquées (9) 122 (2019), 125-163.

  • Dejun Luo, Jian Wang. Coupling by reflection and H?lder regularity for non-local operators of variable order. Transactions of the American Mathematical Society 371 (2019), no. 1, 431-459.

  • Shizan Fang, Dejun Luo. Constantin and Iyer's representation formula for the Navier-Stokes equations on manifolds. Potential Analysis 48 (2018), no. 2, 181-206.

  • Dejun Luo. The It? SDEs and Fokker-Planck equations with Osgood and Sobolev coefficients. Stochastics 90 (2018),
    no. 3, 379-410.
                                           


研究方向

具有弱可微系数的常微分方程和随机微分方程的适定性
随机噪声对某些流体力学方程的正则化效应

学术论文

  1. Exponential convergence in L^p-Wasserstein distance for diffusion processes without uniformly dissipative drift.

    Dejun Luo, Jian Wang. Math. Nachr. 289 (2016), no. 14-15, 1909–1926.

  2. A characterization of the rate of change of ?-entropy via an integral form curvature-dimension condition.

    Dejun Luo. Adv. Geom. 16 (2016), no. 3, 277–290.

  3. A probabilistic proof of the fundamental gap conjecture via the coupling by reflection.

    Fuzhou Gong, Huaiqian Li, Dejun Luo. Potential Anal. 44 (2016), no. 3, 423–442.

  4. H?lder continuity of semigroups for time changed symmetric stable processes.

    Dejun Luo, Jian Wang. Front. Math. China 11 (2016), no. 1, 109–121.

  5. Quasi-invariance of the stochastic flow associated to It?'s SDE with singular time-dependent drift.

    Dejun Luo. J. Theoret. Probab. 28 (2015), no. 4, 1743–1762.

  6. Generalized stochastic flow associated to the It? SDE with partially Sobolev coefficients and its application.

    Dejun Luo. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 14 (2015), no. 2, 535–573.

  7. Stochastic Lagrangian flows on the group of volume-preserving homeomorphisms of the spheres.

    Dejun Luo. Stochastics 87 (2015), no. 4, 680–701.

  8. Harnack inequalities for SDEs with multiplicative noise and non-regular drift.

    Huaiqian Li, Dejun Luo, Jian Wang. Stoch. Dyn. 15 (2015), no. 3, 1550015, 18 pp.

  9. A unified treatment for ODEs under Osgood and Sobolev type conditions.

    Huaiqian Li, Dejun Luo. Bull. Sci. Math. 139 (2015), no. 1, 114–133.

  10. Dimension-independent estimates on the densities of Wiener functionals via the log-Sobolev inequality.

    Dejun Luo. Potential Anal. 41 (2014), no. 3, 903–915.

  11. Uniqueness of degenerate Fokker-Planck equations with weakly differentiable drift whose gradient is given by a singular integral.

    Dejun Luo. Electron. Commun. Probab. 19 (2014), no. 43, 14 pp.

  12. Spectral gaps of Schr?dinger operators and diffusion operators on abstract Wiener spaces.

    Fu-zhou Gong, Yong Liu, Yuan Liu, De-jun Luo. J. Funct. Anal. 266 (2014), no. 9, 5639–5675.

  13. Fokker-Planck type equations with Sobolev diffusion coefficients and BV drift coefficients.

    De Jun Luo. Acta Math. Sin. (Engl. Ser.) 29 (2013), no. 2, 303–314.

  14. Asymptotic estimates on the time derivative of entropy on a Riemannian manifold.

    Adrian P. C. Lim, Dejun Luo. Adv. Geom. 13 (2013), no. 1, 97–115.

  15. Quasi-invariant flow generated by Stratonovich SDE with BV drift coefficient.

    Huaiqian Li, Dejun Luo. Stoch. Anal. Appl. 30 (2012), no. 2, 258–284.

  16. Heat semi-group and generalized flows on complete Riemannian manifolds.

    Shizan Fang, Huaiqian Li, Dejun Luo. Bull. Sci. Math. 135 (2011), no. 6-7, 565–600.

  17. Absolute continuity under flows generated by SDE with measurable drift coefficients.

    Dejun Luo. Stochastic Process. Appl. 121 (2011), no. 10, 2393–2415.

  18. Pathwise uniqueness of multi-dimensional stochastic differential equations with H?lder diffusion coefficients.

    Dejun Luo. Front. Math. China 6 (2011), no. 1, 129–136.

  19. Well-posedness of Fokker-Planck type equations on the Wiener space.

    Dejun Luo. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 13 (2010), no. 2, 273–304.

  20. Stochastic differential equations with coefficients in Sobolev spaces.

    Shizan Fang, Dejun Luo, Anton Thalmaier. J. Funct. Anal. 259 (2010), no. 5, 1129–1168.

  21. Transport equations and quasi-invariant flows on the Wiener space.

    Shizan Fang, Dejun Luo. Bull. Sci. Math. 134 (2010), no. 3, 295–328.

  22. Quasi-invariance of Lebesgue measure under the homeomorphic flow generated by SDE with non-Lipschitz coefficient.

    Dejun Luo. Bull. Sci. Math. 133 (2009), no. 3, 205–228.

  23. Isotropic stochastic flow of homeomorphisms on R d associated with the critical Sobolev exponent.

    Dejun Luo. Stochastic Process. Appl. 118 (2008), no. 8, 1463–1488.

  24. Regularity of solutions to differential equations with non-Lipschitz coefficients.

    Dejun Luo. Bull. Sci. Math. 132 (2008), no. 4, 257–271.

  25. Flow of homeomorphisms and stochastic transport equations.

    Shizan Fang, Dejun Luo. Stoch. Anal. Appl. 25 (2007), no. 5, 1079–1108.


联系方式

地址:北京市海淀区中关村东路55号思源楼608室

邮箱:luodj@amss.ac.cn