个人简介


Dejun Luo, Professor, Academy of Mathematics and Systems Science, Chinese Academy of Sciences


Education

  2005.7--2008.9: PhD, Beijing Normal University and Université de Bourgogne (France) 

  2003.9--2005.7: MS，School of Mathematical Sciences, Beijing Normal University

  1999.9--2003.7: BS，Department of Mathematics, Beijing Normal University

Work Experience

  2022.4--Now: Professor, Academy of Mathematics and Systems Science, CAS

  2018.12--2019.11: Visiting Scholar, Scuola Normale Superiore di Pisa, Italy  

  2017.5--2018.3: Visiting Scholar, Department of Mathematics, University of Pisa, Italy   

  2014.3--2022.3: Associate Professor, Academy of Mathematics and Systems Science, CAS  

  2009.3--2011.2: Post Doc, Mathematics Research Unit, University of Luxembourg   

  2008.7--2014.2: Assistant Professor, Academy of Mathematics and Systems Science, CAS

Honors and Awards

  • 中科院数学与系统科学研究院2021年度“重要科研进展奖”

  • 2021年度中科院青年创新促进会优秀会员

Preprints

  • Franco Flandoli, Dejun Luo. Enhanced dissipation and Lyapunov exponents for stochastic transport-diffusion equations with small molecular diffusivity and small noise intensity, preprint, 2024.

  • Shuaijie Jiao, Dejun Luo. On the pathwise uniqueness of stochastic 2D Euler equations with Kraichnan noise and Lp-data, arXiv:2406.07167.

  • Shuaijie Jiao, Dejun Luo. Well-posedness of stochastic mSQG equations with Kraichnan noise  and L^p data, arXiv:2405.01045.

  • Dejun Luo, Bin Tang, Guohuan Zhao. An elementary approach to mixing and dissipation enhancement by transport noise, arXiv:2402.07484.

  • Chang Liu, Dejun Luo. Finite time mixing and enhanced dissipation for 2D Navier--Stokes equations by Ornstein--Uhlenbeck flow, arXiv:2307.01493.

  • Lucio Galeati, Dejun Luo. Weak well-posedness by transport noise for a class of 2D fluid dynamics equations, arXiv:2305.08761.

  • Dejun Luo. Uniqueness of weak solutions to the limit resonant equation of 3D rotating Navier-Stokes equations, arXiv:2303.09179.

Recent Papers

  • Franco Flandoli, Dejun Luo. Mean field limit of point vortices with environmental noises to deterministic 2D Navier-Stokes equations. Communications in Mathematics and Statistics (2024), accepted, see arXiv:2103.01497.

  • Dejun Luo. Enhanced dissipation for stochastic Navier-Stokes equations with transport noise. Journal of Dynamics and Differential Equations (2023), https://doi.org/10.1007/s10884-023-10307-w.

  • Franco Flandoli, Dejun Luo. On the Boussinesq hypothesis for a stochastic Proudman-Taylor model. SIAM Journal on Mathematical Analysis 56 (2024), no. 3, 3886-3923.

  • Franco Flandoli, Dejun Luo, Eliseo Luongo. 2D Smagorinsky type large eddy models as limits of stochastic PDEs. Journal of Nonlinear Science 34 (2024), no. 3, paper No. 54.

  • Franco Flandoli, Lucio Galeati, Dejun Luo. Quantitative convergence rates for scaling limit of SPDEs with transport noise. Journal of Differential Equations 394 (2024), 237-277.

  • Lucio Galeati, Dejun Luo. LDP and CLT for SPDEs with transport noise. Stochastics and Partial Differential Equations: Analysis and Computations 12 (2024), no. 1, 736-793.

  • Dejun Luo. Regularization by transport noise for 3D MHD equations. Science in China Mathematics 66 (2023), no. 6, 1375-1394.

  • Dejun Luo, Danli Wang. Well posedness and limit theorems for a class of stochastic dyadic models. SIAM Journal on Mathematical Analysis 55 (2023), no. 2, 1464-1498.

  • Dejun Luo, Bin Tang. Stochastic inviscid Leray-alpha model with transport noise: convergence rates and CLT. Nonlinear Analysis 234 (2023), paper no. 113301.

  • Shuchen Guo, Dejun Luo. Scaling Limit of Moderately Interacting Particle Systems with Singular Interaction and Environmental Noise. Annals of Applied Probability 33 (2023), no. 3, 2066-2102.

  • Zhao Dong, Dejun Luo, Bin Tang. Dissipation enhancement by transport noise for stochastic p-Laplace equations. NoDEA Nonlinear Differential Equations Appl. 30 (2023), no. 1, Paper No. 5.

  • Franco Flandoli, Dejun Luo, Cristiano Ricci. Numerical computation of probabilities for nonlinear SDEs in high dimension using Kolmogorov equation. Applied Mathematics and Computation 436 (2023), Paper No. 127520, 17 pp.

  • Franco Flandoli, Dejun Luo. Cristiano Ricci. On the relation between the Girsanov transform and the Kolmogorov equations for SPDEs. Potential Analysis 57 (2022), no. 4, 473-500.

  • Franco Flandoli, Martina Hofmanová, Dejun Luo, Torstein Nilssen. Global well-posedness of the 3D Navier--Stokes equations perturbed by a deterministic vector field. Annals of Applied Probability 32 (2022), no. 4, 2568-2586.

  • Franco Flandoli, Lucio Galeati, Dejun Luo. Eddy heat exchange at the boundary under white noise turbulence. Philosophical Transactions of the Royal Society A 380 (2022), no. 2219, Paper no. 096, 13pp.

  • Dejun Luo. Convergence of stochastic 2D inviscid Boussinesq equations with transport noise to a deterministic viscous system. Nonlinearity 34 (2021), no. 12, 8311-8330.

  • Franco Flandoli, Lucio Galeati, Dejun Luo. Delayed blow-up by transport noise. Communications in Partial Differential Equations 46 (2021), no. 9, 1757-1788.

  • Dejun Luo, Rongchan Zhu. Stochastic mSQG equations with multiplicative transport noises: white noise solutions and scaling limit. Stochastic Processes and their Applications 140 (2021), 236-286.

  • Franco Flandoli, Dejun Luo. High mode transport noise improves vorticity blow-up control in 3D Navier-Stokes equations. Probability Theory and Related Fields 180 (2021), no. 1-2, 309-363. 

  • 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 493 (2021), no. 1, 124505, 29 pp.

  • 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 21 (2021), no. 1, 567-600.

  • Dejun Luo, Martin Saal. Regularization by noise for the point vortex model of mSQG equations. Acta Mathematica Sinica English Series 37 (2021), no. 3, 408-422. 

  • Franco Flandoli, Dejun Luo. Point vortex approximation for 2D Navier-Stokes equations driven by space-time white noise. Journal of Mathematical Analysis and Applications 493 (2021), no. 2, 124560, 21 pp.

  • Franco Flandoli, Francesco Grotto, Dejun Luo. Fokker-Planck equation for dissipative 2D Euler equations with cylindrical noise. Theory of Probability and Mathematical Statistics 102 (2020), 117-143.

  • Dejun Luo, Martin Saal. A scaling limit for the stochastic mSQG equations with multiplicative transport noises. Stochastics and Dynamics 20 (2020), no. 6, 2040001, 21 pp.

  • 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 Holder 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 Ito 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.

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