周道国
姓名: 周道国
职称: 副教授
邮箱: dgzhou@hznu.edu.cn
个人简介:
周道国,男,汉族,1981年生,河南信阳人,理学博士.
2023-至今,杭州师范大学,副教授
2011-2022,河南理工大学,讲师、副教授
2017.11-2018.11,牛津大学数学研究所,访问学者
2008-2011,中科院数学与系统科学研究院应用数学研究所,理学博士
2005-2007, 浙江大学,理学硕士
2000-2004, 河南师范大学,理学学士
研究方向:流体力学中的偏微分方程,特别是千禧年公开问题三维不可压缩Naiver-Stokes方程光滑解的存在性.
教学与课程:
本科生课程: 高等数学,线性代数,概率论与数理统计,概率论与数理统计(双语),复变函数与积分变换,偏微分方程,偏微分方程(双语),分析选讲,高等数学C,复变函数.
研究生课程: 数学物理方程,偏微分方程,泛函分析,索伯列夫空间,不可压缩流导论.
承担课题:
1.国家自然科学基金面上项目,批准号:12071113,不可压缩Navier-Stokes 方程解的正则性,2021-01至2024-12,51万元,在研,主持.
2.国家自然科学基金青年科学基金,批准号:11401176,不可压缩磁流体力学方程的一些数学问题,2015-01至2017-12,23万元,已结题,主持.
3.国家自然科学基金天元基金,批准号:11226169,具有内在自由度的不可压缩流体的数学理论,2013-01至2013-12,3万元,已结题,主持.
学术研究(部分成果):
[1]Shuai Li, Wendong Wang, Daoguo Zhou. Remarks on interior regularity criteria without pressure for the Navier-Stokes equations. J. Differential Equations, 397 (2024), 80–105.
[2]Haifeng Shang, Daoguo Zhou. Optimal decay for the 2D anisotropic Navier-Stokes equations with mixed partial dissipation. Appl. Math. Lett. 144 (2023), Paper No. 108696, 7 pp.
[3]Daoguo Zhou. Regularity criteria in Lorentz spaces for the three dimensional Navier-Stokes equations. Acta Math. Sci. Ser. A (Chinese Ed.) 41 (2021), no. 5, 1396–1404.
[4]Zhouyu Li, Daoguo Zhou. On endpoint regularity criterion of the 3D Navier–Stokes equations. Dynamics of Partial Differential Equations, 18 (2021), no. 1, 71–80.
[5]G. Seregin and Daoguo Zhou. Regularity of solutions to the Navier-Stokes equations in $\dot{B}^{−1}_{\infty,\infty}. Journal of Mathematical Sciences, 244 (2020), no.6, 1003–1009.
[6]Guoliang He, Yanqing Wang, Daoguo Zhou. Lower bounds of blow up solutions in $H^1_p(R3)$ of the Navier–Stokes equations and the quasi-geostrophic equation. Communications in Mathematical Sciences, 18 (2020), no. 8, 2263–2270.
[7]Yanqing Wang, Gang Wu, Daoguo Zhou. Epsilon-regularity criteria in anisotropic Lebesgue spaces and Leray’s self-similar solutions to the 3D Navier-Stokes equations. Zeitschrift für angewandte Mathematik und Physik, 71(5):164, 2020.
[8]Cheng He, Yanqing Wang, Daoguo Zhou. New epsilon-regularity criteria of suitable weak solutions of the 3D Navier-Stokes equations at one scale. Journal of Nonlinear Science, 29(6): 2681–2698, 2019.
[9]Yanqing Wang, Gang Wu, Daoguo Zhou. A regularity criterion at one scale without pressure for suitable weak solutions to the Navier-Stokes equations. Journal of Differential Equations, 267(8):4673–4704, 2019.
[10]Quansen Jiu, Yanqing Wang, Daoguo Zhou. On Wolf’s regularity criterion of suitable weak solutions to the Navier-Stokes equations. Journal of Mathematical Fluid Mechanics, 21(2): Paper No. 22, 16, 2019.
[11]Daoguo Zhou, Zilai Li, Haifeng Shang, Jiahong Wu, Baoquan Yuan, Jiefeng Zhao. Global well-posedness for the 2D fractional Boussinesq equations in the subcritical case. Pacific Journal of Mathematics, 298(1):233–255, 2019.
[12]Yanqing Wang, Gang Wu, Daoguo Zhou. Some interior regularity criteria involving two components for weak solutions to the 3D Navier-Stokes equations. Journal of Mathematical Fluid Mechanics, 20(4):2147–2159, 2018.