管理员登录 / English
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,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“吉林省优秀博士论文”。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,以及北京市自然科学基金—面上项目。现正在主持国家自然科学基金——面上项目。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30余篇,已发表的论文34篇,其中被SCI检索的论文有29篇,其中11篇发表在SIAM J. Math. Anal. ,J. Differential Equations,J. Nonlinear Science以及Nonlinearity杂志上。被引用次数达100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的研究,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.

代表论文

[1]  Global regularity of 3D generalized incompressible magneto- hydrodynamic-α model, accepted by Applied Mathematics Letters, 2014, 1-6.( with Ye Zhuan)

[2]  Time analyticity and backward uniqueness of 2D Boussinesq equations, accepted by Colloquium Math., 2014, 1-11.(with Hou Qianqian)

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

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

[5]  Global regularity of the two-dimensional incompressible generalized magnetohydrodynamics system. Nonlinear Anal. 100 (2014), 86–96. (with Ye Zhuan)

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

[7]  The lifespan of solutions to the inviscid 3D Boussinesq system. Appl. Math. Lett. 26 (2013), 854-859. (with Ye Zhuan)

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

[9]  Local existence and blow-up criterion of the 2-D compressible Boussinesq equations without dissipation terms, Discrete Continuous Dynamical System A, 25(2009), 1333--1347.

[10]  Local well-posedness and ill-posedness for the fractal Burgers equation in homogeneous Sobolev spaces. Math. Methods Appl. Sci. 32 (2009), 359--370.

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

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

[13]  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)

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

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

学生培养

        1位在读博士生, 3位在读硕士生, 1位硕士生已毕业.

对考生说的话

        对数学分析感兴趣,并能持之以恒。