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许孝精
基本介绍
姓名:许孝精
职称:教授
职务:副院长兼副所长
所在部门(教研室):方程
研究方向:偏微分方程及其应用
电子邮件:xjxu@bnu.edu.cn
个人简介

        许孝精,男,教授。2005年在吉林大学获得博士学位,2012年被聘为博士生指导教师。主要从事偏微分方程及其应用方向的研究,重点研究来自流体动力学中的偏微分方程组的适定性。2007年博士论文被评为“吉林省优秀博士学位论文”。主持并完成中国博士后科学基金,国家自然科学基金—青年科学基金,以及国家、北京市自然科学基金—面上项目各1项。现正在主持国家自然科学基金—面上项目1项。曾获北京师范大学励耘优秀青年教师一等奖。与袁洪君教授合作编写本科生教材《数学物理方程》(教育部“十一五”国家级规划教材)一部,完成学术论文50余篇,已发表的论文45篇,其中被SCI检索的论文有40篇,有12篇论文发表在J. Math. Pures Appl., SIAM J. Math. Anal. ,Nonlinearity,J. Nonlinear Science以及J. Differential Equations杂志上。被引用次数达310余次。曾在法国、美国、加拿大、波兰和香港等地区进行学术访问十余次。

研究兴趣

       主要从事来自流体动力学的偏微分方程的适定性研究,主要包括解的存在性,正则性,唯一性和渐进性。

科研项目

[1]  China Postdoctor Sciences Fund, Harmonical analysis and com- pressible Non-Newtonian fluid with vacuum. 2005.12-- 2007. 07.

[2]  NSF of China (Young), Theoretical and numerical analysis on compressible Non-Newtonian fluid. 2007.01--2009.12.

[3]  Program for Changjiang Scholars and innovative Research Team in University, Harmonic analysis and Geometry on manifolds. 2010.1—2012.12. (attended)

[4]  NSF of Beijing, Theory analysis of the non-Newtonian fluids from chymistry industry. 2011.1--2013.12.

[5]  NSF of China, Mathematical Problems of compressible fluids mechanics with the anomalous diffusion. 2014.1--2017.12.

[6] NSF of China, Well-posedness of incompressible fluids mechanics with the anomalous diffusion. 2018.1--2021.12.

 

代表论文

[1] The 2D Boussinesq equations with fractional horizotal dissipation and thermal diffusion, J. Math. Pures Appl., 2017, accepted.with Wu Jiahong and Ye Zhuan)

 

[2] Global well-posedness of the 2D Boussinesq equations with fractional Laplacian dissipation, J. Differential Equations, 260(2016), 6716-6744.( with Ye Zhuan)

 

[3] Global regularity results for the 2D Boussinesq equations with partial dissipation. J. Differential Equations 260 (2016), 1893–1917.(with Adhikari Dhanapati; Cao Chongsheng; Shang Haifeng; Wu Jiahong and Ye Zhuan)

 

[4] Global smooth solutions to thenn-dimensional damped models of incompressible fluid mechanics with small initial datum. J. Nonlinear Sci. 25 (2015), 157–192.(with Wu Jiahong and Ye Zhuan)

 

[5] The 2D magnetohydrodynamic equations with magnetic diffusion. Nonlinearity 28 (2015), 3935–3955.(with Jiu Quansen; Niu Dongjuan; Wu Jiahong and Yu Huan)

 

[6] Global small solution to the 2D MHD system with a velocity damping term. SIAM J. Math. Anal. 47 (2015), 2630–2656.(with Wu Jiahong and Wu Yifei)

 

[7] Small global solutions to the damped two-dimensional Boussinesq equations, J. Differential Equations, 256(2014), 3594--3613. (with Dhanapati Adhikari, Chongsheng Cao, Jiahong Wu)

 

[8] Yudovich type solution for the 2D inviscid Boussinesq system with critical and supercritical dissipation, J. Differential Equations, 256(2014), 3179--3207.(with Xue Liutang)

 

[9] Well-posedness and inviscid limits of the Boussinesq equations with fractional Laplacian dissipationNonlinearity27(2014), 2215~2232.(with Wu Jiahong)

 

[10] Global wellposedness of an inviscid 2D Boussinesq system with nonlinear thermal diffusivity. Dyn. Partial Differ. Equ. 10 (2013), 255–265. (with Li Dong)

 

[11]  Global regularity of solutions of 2D Boussinesq equations with fractional diffusion, Nonlinear analysis, TMA. 72(2010), 677--681.

 

[12]  Existence and uniqueness of solution for a class of non-Newtonian fluids with singularity and vacuum, J. Differential Equations, 245 (2008), 2871--2916 (with Yuan Hongjun)

 

[13] On convergence of solutions of fractal Burgers equation toward rarefaction waves, SIAM J. Math. Anal., 39(2008), 1536--1549. (with Grzegorz Karch, Changxing Miao)

 

[14] Existence of the unique strong solution for a class of non-Newtonian fluids with vacuum. Quart. Appl. Math. 66 (2008), 249--279. (with Hongjun Yuan)

 

[15] On the Cauchy problem for the evolution p-Laplacian equations with gradient term and source, ​J. Differential Equations, 235(2007), 544-585 . (with Cao Chunling, Gao Wenjie, Lian Songzhe and Yuan Hongjun) 

 

学生培养

        2位在读博士生, 4位在读硕士生, 1位博士已毕业,6位硕士生已毕业.