# Prof. Renjun DUAN

**Associate Professor***BSc, MS (Central China Normal University)
PhD (City University of Hong Kong)*

**Address:**

Room 206, Lady Shaw Building,

The Chinese University of Hong Kong,

Shatin, N.T., Hong Kong

The Chinese University of Hong Kong,

Shatin, N.T., Hong Kong

**Tel:**

(852) 3943 7977

**Email:**

**Personal Website:**

**Fields of Interest:**

PDEs related to kinetic and fluid dynamic equations

**Selected Publications:**

- Renjun Duan, Wei-Xi Li, and Lvqiao Liu,
*Gevrey regularity of mild solutions to the non-cutoff Boltzmann equation*. Accepted for publication in Advances in Mathematics, 2021. - Renjun Duan and Shuangqian Liu,
*The Boltzmann equation for uniform shear flow*. Archive for Rational Mechanics and Analysis, 242 (2021), no. 3, 1947-2002. - Renjun Duan and Shuangqian Liu,
*Compressible Navier-Stokes approximation for the Boltzmann equation in bounded domains*. Transactions of the American Mathematical Society, 374 (2021), no. 11, 7867-7924. - Renjun Duan, Dongcheng Yang, and Hongjun Yu,
*Small Knudsen rate of convergence to rarefaction wave for the Landau equation*. Archive for Rational Mechanics and Analysis, 240 (2021), no. 3,1535-1592. - Renjun Duan, Shuangqian Liu, Shota Sakamoto, and Robert M. Strain,
*Global mild solutions of the Landau and non-cutoff Boltzmann equations*. Communications on Pure and Applied Mathematics, 74 (2021), no. 5, 932-1020. - Renjun Duan and Hongjun Yu,
*The Vlasov-Poisson-Landau system near a local Maxwellian*. Advances in Mathematics, 362 (2020), 106956, 83 pp. - Renjun Duan, Feimin Huang, Yong Wang, and Zhu Zhang,
*Effects of soft interaction and non-isothermal boundary upon long-time dynamics of rarefied gas*. Archive for Rational Mechanics and Analysis, 234 (2019), no. 2, 925-1006. - Renjun Duan and Yong Wang,
*The Boltzmann equation with large-amplitude initial data in bounded domains*. Advances in Mathematics, 343 (2019), 36-109. - Renjun Duan and Hongjun Yu,
*The relativistic Boltzmann equation for soft potentials*. Advances in Mathematics, 312 (2017), 315-373. - Renjun Duan, Feimin Huang, Yong Wang and Tong Yang,
*Global well-posedness of the Boltzmann equation with large amplitude initial data*. Archive for Rational Mechanics and Analysis, 225 (2017), no. 1, 375-424. - Renjun Duan, Yuanjie Lei, Tong Yang, and Hui-Jiang Zhao,
*The Vlasov-Maxwell-Boltzmann system near Maxwellians in the whole space with very soft potentials*. Communications in Mathematical Physics, 351 (2017), no. 1, 95-153. - Renjun Duan, Shuangqian Liu and Jiang Xu,
*Global well-posedness in spatially critical Besov space for the Boltzmann equation*. Archive for Rational Mechanics and Analysis, 220 (2016), no. 2, 711-745. - Renjun Duan,
*Global smooth dynamics of a fully ionized plasma with long-range collisions*. Annales de l'Institut Henri Poincare -Analyse non lineaire, 31 (2014), no. 4, 751-778. - Renjun Duan and Shuangqian Liu,
*The Vlasov-Poisson-Boltzmann system without angular cutoff*. Communications in Mathematical Physics, 324 (2013), no. 1, 1-45. - Yoshihiro Ueda, Renjun Duan and Shuichi Kawashima,
*Decay structure for symmetric hyperbolic systems with non-symmetric relaxation and its application*. Archive for Rational Mechanics and Analysis, 205 (2012), no. 1, 239-266. - Renjun Duan and Robert M. Strain,
*Optimal large-time behavior of the Vlasov-Maxwell-Boltzmann system in the whole space*. Communications on Pure and Applied Mathematics, 64 (2011), no. 11, 1497-1546. - Renjun Duan and Robert M. Strain,
*Optimal time decay of the Vlasov-Poisson-Boltzmann system in $R^3$*. Archive for Rational Mechanics and Analysis, 199 (2011), no. 1, 291-328. - Renjun Duan, Alexander Lorz and Peter Markowich,
*Global solutions to the coupled chemotaxis-fluid equations*. Communications in Partial Differential Equations, 35 (2010), no. 9, 1635-1673. - Renjun Duan, Massimo Fornasier and Giuseppe Toscani,
*A kinetic flocking model with diffusions*. Communications in Mathematical Physics, 300 (2010), no. 1, 95-145. - Renjun Duan, Seiji Ukai, Tong Yang and Huijiang Zhao,
*Optimal decay estimates on the linearized Boltzmann equation with time-dependent forces and their applications*. Communications in Mathematical Physics, 277 (2008), no. 1, 189-236.

#### Courses

Course Code | Course Title | Academic Year | Term |
---|---|---|---|

MATH2040A | Linear Algebra II | 2021/22 | 1 |

MATH4240 | Stochastic Processes | 2021/22 | 2 |

Course Code | Course Title | Academic Year | Term |
---|---|---|---|

MATH2040A | Linear Algebra II | 2020/21 | 1 |

MATH4240 | Stochastic Processes | 2020/21 | 2 |

MATH6042 | Topics in Differential Equations II | 2020/21 | 2 |

MATH2040A | Linear Algebra II | 2019/20 | 1 |

MATH4240 | Stochastic Processes | 2019/20 | 2 |

MATH6042A | Topics in Differential Equations II | 2019/20 | 2 |

MATH2040A | Linear Algebra II | 2018/19 | 1 |

MATH4240 | Stochastic Processes | 2018/19 | 2 |

MATH6042 | Topics in Differential Equations II | 2018/19 | 2 |

MATH4240 | Stochastic Processes | 2017/18 | 2 |

MATH6041B | Topics in Differential Equations I | 2017/18 | 2 |

MATH2010A | Advanced Calculus I | 2016/17 | 1 |

MATH4240 | Stochastic Processes | 2016/17 | 2 |

MATH5022 | Theory of Partial Differential Equations | 2016/17 | 2 |

MATH4240 | Stochastic Processes | 2015/16 | 2 |

MATH5022 | Theory of Partial Differential Equations | 2015/16 | 2 |

MATH2010A | Advanced Calculus I | 2014/15 | 1 |

MATH2020B | Advanced Calculus II | 2014/15 | 2 |

MATH4220 | Partial Differential Equations | 2014/15 | 2 |