单敏捷

发布日期:2025-09-01    浏览次数:

研究方向:

调和分析及其在非线性偏微分方程中的应用,特别是非线性色散方程、水波方程的低正则适定性问题和解的整体动态行为。

E-mail: smj@muc.edu.cn

教育经历:

2014.09-2018.12 北京大学 博士

2016.09-2018.02 京都大学 联合培养

2012.09-2014.07 华中科技大学 硕士

2008.09-2012.07 华中科技大学 学士

工作经历:

2023.01- 中央民族大学理学院 副教授

2024.10-2025.10 中央民族大学国际合作处 副处长(挂职)

2020.11-2022.12 中央民族大学理学院 讲师

2019.01-2020.11 中科院数学与系统科学研究院 博士后

发表论文:

1.Dispersive blow-up for solutions to three dimensional generalized Zakharov-Kuznetsov equations. Communications in Nonlinear Science and Numerical Simulation 150 (2025), 108968 (with Y. Ban)

2.Low regularity conservation laws for Fokas-Lenells equation and Camassa-Holm equation. Advances in Nonlinear Analysis 13(1) (2024), 20240014 (with M. Chen, Y. Lu and J. Wang)

3.A priori estimates for the fifth-order modified KdV equations in Besov spaces with low regularity. Journal of Applied Analysis and Computation 13(4) (2023) 2315-2325 (with M. Chen)

4.Resonant decompositions and global well-posedness for 2D Zakharov-Kuznetsov equation in Sobolev spaces of negative indices. J. Differential Equations 355 (2023) 386-436 (with B. Wang and L. Zhang)

5.Local well-posedness and spatial analyticity for the generalized Zakharov-Kuznetsov equation. Nonlinear Analysis: Theory, Methods and Applications 235 (2023) 113344 (with H. Qian)

6.Lower bounds on the radius of spatial analyticity for the 2D generalized Zakharov-Kuznetsov equation. Journal of Mathematical Analysis and Applications 501(2) (2021) 125218 (with L. Zhang)

7.Global well-posedness and global attractor for two-dimensional Zakharov-Kuznetsov equation. Acta Mathematica Sinica, English Series 36(9) (2020), 969-1000

8.Well-posedness for the two-dimensional Zakharov-Kuznetsov equation. Funkcialaj Ekvacioj 63(1) (2020), 67-95

9.Global well-posedness and existence of the global attractor for the Kadomtsev-Petviashvili equation in the anisotropic Sobolev space. Discrete and Continuous Dynamical Systems 40(3) (2020), 1283-1307 (with N. Kishimoto and Y. Tsutsumi)

10.Localization estimate and global attractor for the damped and forced Zakharov-Kuznetsov equation in R2. Dynamics of Partial Differential Equations 16(4) (2019), 317-323 (with N. Kishimoto and Y. Tsutsumi)

科研项目:

2024.01-2027.12 流体动力学中的椭圆型偏微分方程 国家自然科学基金面上项目 参与

2022.01-2024.12 一类色散方程的解的适定性及整体动力学行为研究 国家自然科学基金青年项目 主持

2020.08-2020.11 流体方程和色散方程的长时间动态行为研究 中国博士后科学基金特别资助 主持

2019.05-2020.11 色散方程的长时间行为研究 中国博士后科学基金面上项目 主持

主讲课程:

数学基础(2021,2022)、分析方法(2021,2022)、数学分析(2022)、实变函数(2023,2024)、概率论与数理统计(2023)、线性代数(2024)、高等数学(2023,2024)